TY - JOUR
T1 - The complete classification of a class of conformally flat Lorentzian hypersurfaces in R41
AU - Xie, Zhenxiao
AU - Wang, Changping
AU - Wang, Xiaozhen
PY - 2017/12/1
Y1 - 2017/12/1
N2 - A three-dimensional Lorentzian hypersurface x : M3 1 → R41 is called conformally flat if its induced metric is conformal to the flat Lorentzian metric, this property is preserved under the conformal transformation of R41 . In this paper, using the projective light-cone model, we give a complete classification of those ones whose shape operators have two distinct real eigenvalues and cannot be diagonalizable. These hypersurfaces are conformal equivalent to cones, cylinders, or rotational hypersurfaces generated by B-scrolls (over null Frenet curves) in three-dimensional Lorentzian space forms.
AB - A three-dimensional Lorentzian hypersurface x : M3 1 → R41 is called conformally flat if its induced metric is conformal to the flat Lorentzian metric, this property is preserved under the conformal transformation of R41 . In this paper, using the projective light-cone model, we give a complete classification of those ones whose shape operators have two distinct real eigenvalues and cannot be diagonalizable. These hypersurfaces are conformal equivalent to cones, cylinders, or rotational hypersurfaces generated by B-scrolls (over null Frenet curves) in three-dimensional Lorentzian space forms.
KW - B-scrolls
KW - Conformal geometry of lorentzian space forms
KW - Conformally flat lorentzian hypersurfaces
KW - Nondiagonalizable shape operator
UR - https://www.scopus.com/pages/publications/85038108805
U2 - 10.1142/S0129167X17500926
DO - 10.1142/S0129167X17500926
M3 - 文章
AN - SCOPUS:85038108805
SN - 0129-167X
VL - 28
JO - International Journal of Mathematics
JF - International Journal of Mathematics
IS - 13
M1 - 1750092
ER -