On hypersurfaces in a locally affine Riemannian Banach manifold. II
type: Item
instance of: scholarly article
title: On hypersurfaces in a locally affine Riemannian Banach manifold. II
zbMATH Open document ID: 1071.53033
DOI: 10.1155/S0161171204203325
author: El-Said R. Lashin
author: Tarek Fathy Mersal
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2005-05-18T00:00:00Z
full work available at URL: https://eudml.org/doc/51646
review text: Summary: In our previous work [ibid. 31, No. 6, 275--379 (2002; Zbl 1021.53031)], we proved that an essential second-order hypersurface in an infinite-dimensional locally affine Riemannian Banach manifold is a Riemannian manifold of constant nonzero curvature. In this note, we prove the converse, in other words, we prove that a hypersurface of constant nonzero Riemannian curvature in a locally affine (flat) semi-Riemannian Banach space is an essential hypersurface of second order.
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 58B20
zbMATH DE Number: 2168602
zbMATH Keywords: essential second-order hypersurface
zbMATH Keywords: Riemannian Banach manifold
zbMATH Keywords: constant nonzero curvature
Wikidata QID: Q115243334
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2168602