Semi-Riemannian hypersurfaces in Ln+1 with a totally geodesic foliation of codimension one

被引：0

作者：

Kashani, S. M. B. ^{[1
]}

Vanaei, M. J. ^{[1
]}

Yaghoobi, S. M. ^{[1
]}

机构：

[1] Tarbiat Modares Univ, Fac Math Sci, Dept Pure Math, POB 14115-134, Tehran, Iran

来源：

JOURNAL OF GEOMETRY | 2019年 / 110卷 / 02期

关键词：

Minkowski space; semi-Riemannian hypersurface; totally geodesic foliation; partial tube; relative nullity;

D O I：

10.1007/s00022-019-0477-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We classify hypersurfaces of the Minkowski space Ln+1 that carry a totally geodesic foliation with complete leaves of codimension one. We prove that such a hypersurface is ruled, or a partial tube over a curve or contains a two or three dimensional strip. Moreover, if the hypersurface is embedded then it is a partial tube over a curve.

引用

页数：12

共 50 条

[1] Euclidean hypersurfaces with a totally geodesic foliation of codimension one
M. Dajczer
V. Rovenski
R. Tojeiro
Geometriae Dedicata, 2015, 176 : 215 - 224
[2] Euclidean hypersurfaces with a totally geodesic foliation of codimension one
Dajczer, M.
Rovenski, V.
Tojeiro, R.
GEOMETRIAE DEDICATA, 2015, 176 (01) : 215 - 224
[3] Semi-riemannian submersions with totally geodesic fibres
Baditoiu, G
TOHOKU MATHEMATICAL JOURNAL, 2004, 56 (02) : 179 - 204
[4] Notes on totally geodesic foliations of a complete semi-Riemannian manifold
Shin, An Sook
Han, Hyelim
Kim, Hobum
TURKISH JOURNAL OF MATHEMATICS, 2023, 47 (02) : 528 - 536
[5] Semi-Riemannian hypersurfaces in Ln+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {L}^{n+1}$$\end{document} with a totally geodesic foliation of codimension one
S. M. B. Kashani
M. J. Vanaei
S. M. Yaghoobi
Journal of Geometry, 2019, 110 (2)
[6] CMC Hypersurfaces on Riemannian and Semi-Riemannian Manifolds
Perdomo, Oscar M.
MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY, 2012, 15 (01) : 17 - 37
[7] CMC Hypersurfaces on Riemannian and Semi-Riemannian Manifolds
Oscar M. Perdomo
Mathematical Physics, Analysis and Geometry, 2012, 15 : 17 - 37
[8] Geodesic connectedness of semi-Riemannian manifolds
Sánchez, M
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2001, 47 (05) : 3085 - 3102
[9] GEODESIC REFLECTIONS IN SEMI-RIEMANNIAN GEOMETRY
GARCIARIO, E
VAZQUEZABAL, ME
CZECHOSLOVAK MATHEMATICAL JOURNAL, 1993, 43 (04) : 583 - 597
[10] Hypersurfaces of space forms carrying a totally geodesic foliation
Marcos Dajczer
Ruy Tojeiro
Geometriae Dedicata, 2020, 205 : 129 - 146

← 1 2 3 4 5 →