TY - JOUR
T1 - Laguerre isopararmetric hypersurfaces in ℝ 4
AU - Li, Tong Zhu
AU - Sun, Hua Fei
PY - 2012/6
Y1 - 2012/6
N2 - Let x : M → ℝ n be an umbilical free hypersurface with non-zero principal curvatures. Then x is associated with a Laguerre metric g, a Laguerre tensor L, a Laguerre form C, and a Laguerre second fundamental form B which are invariants of x under Laguerre transformation group. A hypersurface x is called Laguerre isoparametric if its Laguerre form vanishes and the eigenvalues of B are constant. In this paper, we classify all Laguerre isoparametric hypersurfaces in ℝ 4.
AB - Let x : M → ℝ n be an umbilical free hypersurface with non-zero principal curvatures. Then x is associated with a Laguerre metric g, a Laguerre tensor L, a Laguerre form C, and a Laguerre second fundamental form B which are invariants of x under Laguerre transformation group. A hypersurface x is called Laguerre isoparametric if its Laguerre form vanishes and the eigenvalues of B are constant. In this paper, we classify all Laguerre isoparametric hypersurfaces in ℝ 4.
KW - Laguerre isoparametric hypersurface
KW - Laguerre second fundamental form
KW - Laguerre transformation group
UR - http://www.scopus.com/inward/record.url?scp=84860750973&partnerID=8YFLogxK
U2 - 10.1007/s10114-011-0322-2
DO - 10.1007/s10114-011-0322-2
M3 - Article
AN - SCOPUS:84860750973
SN - 1439-8516
VL - 28
SP - 1179
EP - 1186
JO - Acta Mathematica Sinica, English Series
JF - Acta Mathematica Sinica, English Series
IS - 6
ER -