TY - JOUR
T1 - Rigidity of closed minimal hypersurfaces in S5
AU - Cheng, Pengpeng
AU - Li, Tongzhu
N1 - Publisher Copyright:
© 2025 Elsevier B.V.
PY - 2025/9
Y1 - 2025/9
N2 - Let M4→S5 be a closed immersed minimal hypersurface with constant squared length of the second fundamental form S in a 5-dimensional sphere S5. In this paper, we prove that if the 3-mean curvature H3 and the number g of the distinct principal curvatures are constant, then M4 is an isoparametric hypersurface, and the value of S can only be 0,4,12. This result supports Chern Conjecture.
AB - Let M4→S5 be a closed immersed minimal hypersurface with constant squared length of the second fundamental form S in a 5-dimensional sphere S5. In this paper, we prove that if the 3-mean curvature H3 and the number g of the distinct principal curvatures are constant, then M4 is an isoparametric hypersurface, and the value of S can only be 0,4,12. This result supports Chern Conjecture.
KW - Chern conjecture
KW - Isoparametric hypersurfaces
KW - Minimal hypersurfaces
KW - The second fundamental form
UR - https://www.scopus.com/pages/publications/105004456721
U2 - 10.1016/j.difgeo.2025.102252
DO - 10.1016/j.difgeo.2025.102252
M3 - Article
AN - SCOPUS:105004456721
SN - 0926-2245
VL - 100
JO - Differential Geometry and its Application
JF - Differential Geometry and its Application
M1 - 102252
ER -