Research output per year
Research output per year
Personal profile
Personal profile
Li Tongzhu Job Title: Professor E-mail: litz@bit.edu.cn
My research interests are in the geometry of submanifolds (Lie sphere geometry of major submanifolds, Moebius geometry of submanifolds, Laguerre geometry of submanifolds and isometric group geometry of neutron manifolds in space of constant curvature) and the large-scale geometry of Riemannian manifolds. Presided over the National Natural Science Foundation of 4, participated in the National Natural Science Foundation of 4, participated in the Ministry of Science and Technology key research and development project. He has published more than 40 academic papers in professional journals of mathematics at home and abroad. He won one of the first prizes of the 2014 Scientific Research Outstanding Achievement Award (Nature category) of the Ministry of Education.
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My research interests are in the geometry of submanifolds (Lie sphere geometry of major submanifolds, Moebius geometry of submanifolds, Laguerre geometry of submanifolds and isometric group geometry of neutron manifolds in space of constant curvature) and the large-scale geometry of Riemannian manifolds. Presided over the National Natural Science Foundation of 4, participated in the National Natural Science Foundation of 4, participated in the Ministry of Science and Technology key research and development project. He has published more than 40 academic papers in professional journals of mathematics at home and abroad. He won one of the first prizes of the 2014 Scientific Research Outstanding Achievement Award (Nature category) of the Ministry of Education.
More
Research Interests
Submanifold geometry and large-scale Riemannian manifold geometry and topology.
Education
2005 PhD, School of Mathematical Sciences, Peking University
Professional Experience
June 2005 -- June 2007, Lecturer, Department of Mathematics, Beijing Institute of Technology,
July 2007 - June 2009, Postdoctoral fellow, Department of Mathematics, Capital Normal University.
June 2009 -- June 2012, Department of Mathematics, Beijing Institute of Technology, Lecturer,
July 2012 -- January 2014, Associate Professor, Department of Mathematics, Beijing Institute of Technology,
2014/02-2015/02, Visiting Researcher, Department of Mathematics, University of California, St. Creutz,
2015/03-- 2018/06, Associate Professor, Department of Mathematics, Beijing Institute of Technology,
2018/07 - Now, Professor, Department of Mathematics, Beijing Institute of Technology.
July 2007 - June 2009, Postdoctoral fellow, Department of Mathematics, Capital Normal University.
June 2009 -- June 2012, Department of Mathematics, Beijing Institute of Technology, Lecturer,
July 2012 -- January 2014, Associate Professor, Department of Mathematics, Beijing Institute of Technology,
2014/02-2015/02, Visiting Researcher, Department of Mathematics, University of California, St. Creutz,
2015/03-- 2018/06, Associate Professor, Department of Mathematics, Beijing Institute of Technology,
2018/07 - Now, Professor, Department of Mathematics, Beijing Institute of Technology.
Research Achievement
[42] ,姬秀; 李同柱，Lorentz空间中的Para-isotropic超曲面. (Chinese) 数学学报（中文版） 64 (2021), no. 1, 47–58.
[41],Xie, Zhenxiao; Li, Tongzhu; Ma, Xiang; Wang, Changping ,Wintgen ideal submanifolds: new examples, frame sequence and Möbius homogeneous classification.
Adv. Math. 381 (2021), Paper No. 107620, 31 pp.
[40], Ji, Xiu; Li, Tongzhu ,Conformal homogeneous spacelike hypersurfaces with two distinct principal curvatures in Lorentzian space forms.
Houston J. Math. 46 (2020), no. 4, 935–951.
[39], Chen, Ya Yun; Ji, Xiu; Li, Tong Zhu, Möbius homogeneous hypersurfaces with one simple principal curvature in Sn+1.
Acta Math. Sin. (Engl. Ser.) 36 (2020), no. 9,
[38], Ji, Xiu; Li, Tongzhu ,Conformal homogeneous spacelike surfaces in 3-dimensional Lorentz space forms.
Differential Geom. Appl. 73 (2020), 101667, 16 pp.
[37], Deng, Zonggang; Li, Tongzhu, Conformally flat Willmore spacelike hypersurfaces in Rn+11.
Turkish J. Math. 44 (2020), no. 1, 252–273.
[36], Lin, Limiao; Li, Tongzhu ,A Möbius rigidity of compact Willmore hypersurfaces in Sn+1.
J. Math. Anal. Appl. 484 (2020), no. 1, 123707, 15 pp.
[35], Ji, Xiu; Li, Tongzhu; Sun, Huafei ,Para-Blaschke isoparametric spacelike hypersurfaces in Lorentzian space forms.
Houston J. Math. 45 (2019), no. 3, 685–706.
[34], Ji, Xiu; Li, Tongzhu; Sun, Huafei, Spacelike hypersurfaces with constant conformal sectional curvature in Rn+11.
Pacific J. Math. 300 (2019), no. 1, 17–37.
[33], Ji, Xiu; Li, TongZhu , A note on compact Móbius homogeneous submanifolds in Sn+1.
Bull. Korean Math. Soc. 56 (2019), no. 3,
[32],陈芝红;李同柱 , 空间形式中紧超曲面的刚性，数学进展，47 (2018), no. 5, 773–778.
[31], Lin, Limiao; Li, Tongzhu; Wang, Changping ，A Möbius scalar curvature rigidity on compact conformally flat hypersurfaces in Sn+1.
J. Math. Anal. Appl. 466 (2018), no. 1, 762–775
[30], Li, Tongzhu; Nie, Changxiong ，Spacelike Dupin hypersurfaces in Lorentzian space forms.
J. Math. Soc. Japan 70 (2018), no. 2, 463–480.
[29], Xie, Zhenxiao; Li, Tongzhu; Ma, Xiang; Wang, Changping ，Wintgen ideal submanifolds: reduction theorems and a coarse classification.
Ann. Global Anal. Geom. 53 (2018), no. 3, 377–403.
[28], Li, Tongzhu， Möbius homogeneous hypersurfaces with three distinct principal curvatures in Sn+1.
Chinese Ann. Math. Ser. B 38 (2017), no. 5, 1131–1144.
[27], Li, Tongzhu; Qing, Jie; Wang, Changping ，Möbius curvature, Laguerre curvature and Dupin hypersurface.
Adv. Math. 311 (2017), 249–294.
[26], Li, Tongzhu; Ma, Xiang; Wang, Changping; Xie, Zhenxiao， Wintgen ideal submanifolds of codimension two, complex curves, and Möbius geometry.
Tohoku Math. J. (2) 68 (2016), no. 4, 621–638.
[25], Guo, Zhen; Li, Tongzhu; Wang, Changping， Classification of hypersurfaces with constant Möbius Ricci curvature in Rn+1.
Tohoku Math. J. (2) 67 (2015), no. 3, 383–403.
[24], Li, Tongzhu; Ma, Xiang; Wang, Changping ，Wintgen ideal submanifolds with a low-dimensional integrable distribution.
Front. Math. China 10 (2015), no. 1, 111–136.
[23], 李同柱; 聂昌雄， 四维球面空间中共形高斯映射调和 的超曲面，数学学报， 57 (2014), no. 6, 1231–1240.
[22], Li, Tongzhu; Wang, Changping ，Classification of Möbius homogeneous hypersurfaces in a 5-dimensional sphere.
Houston J. Math. 40 (2014), no. 4, 1127–1146.
[21], Li, Tongzhu; Wang, Changping ，A note on Blaschke isoparametric hypersurfaces.
Internat. J. Math. 25 (2014), no. 12, 1450117, 9 pp.
[20], Xie, ZhenXiao; Li, TongZhu; Ma, Xiang; Wang, ChangPing， Möbius geometry of three-dimensional Wintgen ideal submanifolds in S5.
Sci. China Math. 57 (2014), no. 6, 1203–1220.
[19], Li, Tongzhu; Ma, Xiang; Wang, Changping， Deformation of hypersurfaces preserving the Möbius metric and a reduction theorem.
Adv. Math. 256 (2014), 156–205.
[18], Li, Tongzhu， Compact Willmore hypersurfaces with two distinct principal curvatures in Sn+1.
Differential Geom. Appl. 32 (2014), 35–45.
[17], Li, Tongzhu; Ma, Xiang; Wang, Changping， Willmore hypersurfaces with constant Möbius curvature in Rn+1.
Geom. Dedicata 166 (2013), 251–267.
[16], Li, Tongzhu; Ma, Xiang; Wang, Changping， Möbius homogeneous hypersurfaces with two distinct principal curvatures in Sn+1.
Ark. Mat. 51 (2013), no. 2, 315–328.
[15], Li, Tongzhu ，Willmore hypersurfaces with two distinct principal curvatures in Rn+1.
Pacific J. Math. 256 (2012), no. 1, 129–149.
[14], Li, TongZhu， Laguerre homogeneous surfaces in R3.
Sci. China Math. 55 (2012), no. 6, 1197–1214.
[13], Guo, Zhen; Li, Tongzhu; Lin, Limiao; Ma, Xiang; Wang, Changping， Classification of hypersurfaces with constant Möbius curvature in Sm+1.
Math. Z. 271 (2012), no. 1-2, 193–219.
[12], Li, Tong Zhu; Sun, Hua Fei， Laguerre isoparametric hypersurfaces in R4.
Acta Math. Sin. (Engl. Ser.) 28 (2012), no. 6, 1179–1186.
[11], Li, TongZhu; Li, HaiZhong; Wang, ChangPing， Classification of hypersurfaces with constant Laguerre eigenvalues in Rn.
Sci. China Math. 54 (2011), no. 6, 1129–1144.
[10], Li, Tongzhu， Homogeneous surfaces in Lie sphere geometry.
Geom. Dedicata 149 (2010), 15–43.
[9], Nie, ChangXiong; Li, TongZhu; He, YiJun; Wu, ChuanXi， Conformal isoparametric hypersurfaces with two distinct conformal principal curvatures in conformal space.
Sci. China Math. 53 (2010), no. 4, 953–965.
[8], Li, Tongzhu; Li, Haizhong; Wang, Changping ，Classification of hypersurfaces with parallel Laguerre second fundamental form in Rn.
Differential Geom. Appl. 28 (2010), no. 2,
[7], 李同柱; 孙华飞， 球面中具有调和曲率的超曲面. 数学进展 37 (2008), no. 1, 57–66.
[6], Li, Tongzhu; Peng, Linyu; Sun, Huafei， The geometric structure of the inverse gamma distribution.
Beiträge Algebra Geom. 49 (2008), no. 1, 217–225.
[5], Li, Tongzhu; Wang, Changping， Laguerre geometry of hypersurfaces in Rn.
Manuscripta Math. 122 (2007), no. 1, 73–95.
[4], Li, Tong Zhu ，Laguerre geometry of surfaces in R3.
Acta Math. Sin. (Engl. Ser.) 21 (2005), no. 6, 1525–1534.
[3], Li Tongzhu, Nie Changxiong, Conformal geometry of hypersurfaces in Lorentz space forms,
Geometry, 2013, Vol.2013, Article ID 549602.
[2], Li Tongzhu, Demeter Krupka, The Geometry of Tangent Bundles: Canonical Vector Fields,
Geometry, 2013, Vol.2013, Article ID 364301.
[1] 李同柱，郭震， 常曲率流形中具平行李奇曲率的超曲面，
数学学报，2004, 47 ,587—592.
[41],Xie, Zhenxiao; Li, Tongzhu; Ma, Xiang; Wang, Changping ,Wintgen ideal submanifolds: new examples, frame sequence and Möbius homogeneous classification.
Adv. Math. 381 (2021), Paper No. 107620, 31 pp.
[40], Ji, Xiu; Li, Tongzhu ,Conformal homogeneous spacelike hypersurfaces with two distinct principal curvatures in Lorentzian space forms.
Houston J. Math. 46 (2020), no. 4, 935–951.
[39], Chen, Ya Yun; Ji, Xiu; Li, Tong Zhu, Möbius homogeneous hypersurfaces with one simple principal curvature in Sn+1.
Acta Math. Sin. (Engl. Ser.) 36 (2020), no. 9,
[38], Ji, Xiu; Li, Tongzhu ,Conformal homogeneous spacelike surfaces in 3-dimensional Lorentz space forms.
Differential Geom. Appl. 73 (2020), 101667, 16 pp.
[37], Deng, Zonggang; Li, Tongzhu, Conformally flat Willmore spacelike hypersurfaces in Rn+11.
Turkish J. Math. 44 (2020), no. 1, 252–273.
[36], Lin, Limiao; Li, Tongzhu ,A Möbius rigidity of compact Willmore hypersurfaces in Sn+1.
J. Math. Anal. Appl. 484 (2020), no. 1, 123707, 15 pp.
[35], Ji, Xiu; Li, Tongzhu; Sun, Huafei ,Para-Blaschke isoparametric spacelike hypersurfaces in Lorentzian space forms.
Houston J. Math. 45 (2019), no. 3, 685–706.
[34], Ji, Xiu; Li, Tongzhu; Sun, Huafei, Spacelike hypersurfaces with constant conformal sectional curvature in Rn+11.
Pacific J. Math. 300 (2019), no. 1, 17–37.
[33], Ji, Xiu; Li, TongZhu , A note on compact Móbius homogeneous submanifolds in Sn+1.
Bull. Korean Math. Soc. 56 (2019), no. 3,
[32],陈芝红;李同柱 , 空间形式中紧超曲面的刚性，数学进展，47 (2018), no. 5, 773–778.
[31], Lin, Limiao; Li, Tongzhu; Wang, Changping ，A Möbius scalar curvature rigidity on compact conformally flat hypersurfaces in Sn+1.
J. Math. Anal. Appl. 466 (2018), no. 1, 762–775
[30], Li, Tongzhu; Nie, Changxiong ，Spacelike Dupin hypersurfaces in Lorentzian space forms.
J. Math. Soc. Japan 70 (2018), no. 2, 463–480.
[29], Xie, Zhenxiao; Li, Tongzhu; Ma, Xiang; Wang, Changping ，Wintgen ideal submanifolds: reduction theorems and a coarse classification.
Ann. Global Anal. Geom. 53 (2018), no. 3, 377–403.
[28], Li, Tongzhu， Möbius homogeneous hypersurfaces with three distinct principal curvatures in Sn+1.
Chinese Ann. Math. Ser. B 38 (2017), no. 5, 1131–1144.
[27], Li, Tongzhu; Qing, Jie; Wang, Changping ，Möbius curvature, Laguerre curvature and Dupin hypersurface.
Adv. Math. 311 (2017), 249–294.
[26], Li, Tongzhu; Ma, Xiang; Wang, Changping; Xie, Zhenxiao， Wintgen ideal submanifolds of codimension two, complex curves, and Möbius geometry.
Tohoku Math. J. (2) 68 (2016), no. 4, 621–638.
[25], Guo, Zhen; Li, Tongzhu; Wang, Changping， Classification of hypersurfaces with constant Möbius Ricci curvature in Rn+1.
Tohoku Math. J. (2) 67 (2015), no. 3, 383–403.
[24], Li, Tongzhu; Ma, Xiang; Wang, Changping ，Wintgen ideal submanifolds with a low-dimensional integrable distribution.
Front. Math. China 10 (2015), no. 1, 111–136.
[23], 李同柱; 聂昌雄， 四维球面空间中共形高斯映射调和 的超曲面，数学学报， 57 (2014), no. 6, 1231–1240.
[22], Li, Tongzhu; Wang, Changping ，Classification of Möbius homogeneous hypersurfaces in a 5-dimensional sphere.
Houston J. Math. 40 (2014), no. 4, 1127–1146.
[21], Li, Tongzhu; Wang, Changping ，A note on Blaschke isoparametric hypersurfaces.
Internat. J. Math. 25 (2014), no. 12, 1450117, 9 pp.
[20], Xie, ZhenXiao; Li, TongZhu; Ma, Xiang; Wang, ChangPing， Möbius geometry of three-dimensional Wintgen ideal submanifolds in S5.
Sci. China Math. 57 (2014), no. 6, 1203–1220.
[19], Li, Tongzhu; Ma, Xiang; Wang, Changping， Deformation of hypersurfaces preserving the Möbius metric and a reduction theorem.
Adv. Math. 256 (2014), 156–205.
[18], Li, Tongzhu， Compact Willmore hypersurfaces with two distinct principal curvatures in Sn+1.
Differential Geom. Appl. 32 (2014), 35–45.
[17], Li, Tongzhu; Ma, Xiang; Wang, Changping， Willmore hypersurfaces with constant Möbius curvature in Rn+1.
Geom. Dedicata 166 (2013), 251–267.
[16], Li, Tongzhu; Ma, Xiang; Wang, Changping， Möbius homogeneous hypersurfaces with two distinct principal curvatures in Sn+1.
Ark. Mat. 51 (2013), no. 2, 315–328.
[15], Li, Tongzhu ，Willmore hypersurfaces with two distinct principal curvatures in Rn+1.
Pacific J. Math. 256 (2012), no. 1, 129–149.
[14], Li, TongZhu， Laguerre homogeneous surfaces in R3.
Sci. China Math. 55 (2012), no. 6, 1197–1214.
[13], Guo, Zhen; Li, Tongzhu; Lin, Limiao; Ma, Xiang; Wang, Changping， Classification of hypersurfaces with constant Möbius curvature in Sm+1.
Math. Z. 271 (2012), no. 1-2, 193–219.
[12], Li, Tong Zhu; Sun, Hua Fei， Laguerre isoparametric hypersurfaces in R4.
Acta Math. Sin. (Engl. Ser.) 28 (2012), no. 6, 1179–1186.
[11], Li, TongZhu; Li, HaiZhong; Wang, ChangPing， Classification of hypersurfaces with constant Laguerre eigenvalues in Rn.
Sci. China Math. 54 (2011), no. 6, 1129–1144.
[10], Li, Tongzhu， Homogeneous surfaces in Lie sphere geometry.
Geom. Dedicata 149 (2010), 15–43.
[9], Nie, ChangXiong; Li, TongZhu; He, YiJun; Wu, ChuanXi， Conformal isoparametric hypersurfaces with two distinct conformal principal curvatures in conformal space.
Sci. China Math. 53 (2010), no. 4, 953–965.
[8], Li, Tongzhu; Li, Haizhong; Wang, Changping ，Classification of hypersurfaces with parallel Laguerre second fundamental form in Rn.
Differential Geom. Appl. 28 (2010), no. 2,
[7], 李同柱; 孙华飞， 球面中具有调和曲率的超曲面. 数学进展 37 (2008), no. 1, 57–66.
[6], Li, Tongzhu; Peng, Linyu; Sun, Huafei， The geometric structure of the inverse gamma distribution.
Beiträge Algebra Geom. 49 (2008), no. 1, 217–225.
[5], Li, Tongzhu; Wang, Changping， Laguerre geometry of hypersurfaces in Rn.
Manuscripta Math. 122 (2007), no. 1, 73–95.
[4], Li, Tong Zhu ，Laguerre geometry of surfaces in R3.
Acta Math. Sin. (Engl. Ser.) 21 (2005), no. 6, 1525–1534.
[3], Li Tongzhu, Nie Changxiong, Conformal geometry of hypersurfaces in Lorentz space forms,
Geometry, 2013, Vol.2013, Article ID 549602.
[2], Li Tongzhu, Demeter Krupka, The Geometry of Tangent Bundles: Canonical Vector Fields,
Geometry, 2013, Vol.2013, Article ID 364301.
[1] 李同柱，郭震， 常曲率流形中具平行李奇曲率的超曲面，
数学学报，2004, 47 ,587—592.
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Research output
- 41 Article
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Local rigidity of constant mean curvature hypersurfaces in space forms
Chen, Y. & Li, T., 15 Mar 2025, In: Journal of Mathematical Analysis and Applications. 543, 2P1, 128974.Research output: Contribution to journal › Article › peer-review
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Classification of Möbius homogeneous curves in R4
Li, T. & Lin, R., 2024, In: AIMS Mathematics. 9, 8, p. 23027-23046 20 p.Research output: Contribution to journal › Article › peer-review
Open Access -
Möbius homogeneous hypersurfaces in Sn+1
Li, T., Ma, X., Wang, C. & Wang, P., Jun 2024, In: Advances in Mathematics. 448, 109722.Research output: Contribution to journal › Article › peer-review
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Classification of spacelike conformal Einstein hypersurfaces in Lorentzian space Rn+1 1
Chen, Y. & Li, T., 2023, In: AIMS Mathematics. 8, 10, p. 23247-23271 25 p.Research output: Contribution to journal › Article › peer-review
Open Access -
The Global Property of Generic Conformally Flat Hypersurfaces in R4
Chen, Y. & Li, T., Mar 2023, In: Mathematics. 11, 6, 1435.Research output: Contribution to journal › Article › peer-review
Open Access