Degenerate submanifolds in semi-Riemannian geometry
type: Item
instance of: scholarly article
title: Degenerate submanifolds in semi-Riemannian geometry
zbMATH Open document ID: 0644.53019
DOI: 10.1007/BF00181606
published in: Geometriae Dedicata
publication date: 1987-01-01T00:00:00Z
review text: Let (M,g) be a semi-Riemannian manifold of arbitrary signature and (H,g\(| H)\) be a degenerate submanifold of M, i.e. \(g| H\) is singular and has constant signature. In this paper the author extends his studies on null submanifolds of Lorentzian manifolds [ibid. 23, 33-51 (1987; Zbl 0625.53019)] to the situation described above by employing his results on degenerate manifolds [ibid. 23, 259-290 (1987; Zbl 0625.53020)]. The main problem is that there does not exist a natural projection (as in the nondegenerate case) onto the tangent space of a degenerate submanifold. Nevertheless the author succeeds in showing the usual compatibility of the induced singular semi-Riemannian structure of H with the semi-Riemannian structure of M for a certain subclass the so- called irrational stationary degenerate submanifolds. In this case Gauss- Codazzi equations are obtained. Furthermore at the end of the paper the property of total umbilicity is investigated for this type of submanifolds.
Mathematics Subject Classification ID: 53B25
Mathematics Subject Classification ID: 53B30
zbMATH DE Number: 4050449
zbMATH Keywords: degenerate submanifold
zbMATH Keywords: singular semi-Riemannian structure
zbMATH Keywords: irrational stationary degenerate submanifolds
zbMATH Keywords: Gauss-Codazzi equations
zbMATH Keywords: total umbilicity
author: Demir N. Kupeli
reviewed by: Bernd Wegner
MaRDI profile type: Publication
Recommended article: Q4390756
Recommended article: Q4305551
Recommended article: On the structure of submanifolds with degenerate Gauss maps
Recommended article: Q4427608
Recommended article: Submanifolds with degenerate Gauss mappings in spheres
Recommended article: Degenerate manifolds
Recommended article: Q3223494
Recommended article: Q4263183
Recommended article: Q5545212
Recommended article: Q5753146
description: scientific article; zbMATH DE number 4050449