A parametrization of isometric immersions between anti-de Sitter space-times
type: Item
instance of: scholarly article
title: A parametrization of isometric immersions between anti-de Sitter space-times
zbMATH Open document ID: 0918.53020
author: Kinetsu Abe
author: Hiroshi Mori
published in: Kodai Mathematical Journal
publication date: 1999-08-23T00:00:00Z
review text: The anti-de Sitter space forms of constant curvature \(-1\) are considered. If \(\widetilde H^n_1\) denotes the universal pseudo-Riemannian covering manifold of the \(n\)-dimensional anti-de Sitter spacetime \(H^n_1\), a complete description of the space of isometric immersions of \(\widetilde H^n_1\) into \(\widetilde H^{n+1}_1\) is given. The main result essentially states that for each isometric immersion \(f: \widetilde H^n_1\to\widetilde H^{n+1}_1\) there exists a family of countable \(n\)-tuples of real-valued \(C^\infty\) functions which completely describe the second fundamental form of the immersion and hence the immersion itself. Conversely, there exists an isometric immersion \(f:\widetilde H^n_1\to\widetilde H^{n+1}_1\) whose relative nullity foliation is completely determined by functions in a certain family of \(C^\infty\) functions.
reviewed by: A. P. Stone
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C50
zbMATH DE Number: 1180764
zbMATH Keywords: universal pseudo-Riemannian covering manifold
zbMATH Keywords: anti-de Sitter spacetime
zbMATH Keywords: isometric immersions
zbMATH Keywords: second fundamental form
zbMATH Keywords: relative nullity foliation
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138043792
OpenAlex ID: W2061384160
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DOI: 10.2996/KMJ/1138043792
description: scientific article; zbMATH DE number 1180764