Normally flat Ric-semisymmetric submanifolds in Euclidean spaces
type: Item
instance of: scholarly article
title: Normally flat Ric-semisymmetric submanifolds in Euclidean spaces
zbMATH Open document ID: 1264.53023
DOI: 10.3103/S1066369X12090034
author: V. A. Mirzoyan
author: G. S. Machkalyan
published in: Russian Mathematics
publication date: 2013-03-22T00:00:00Z
review text: Consider a Riemannian manifold \(M\) with Riemann curvature tensor \(R\) and Ricci tensor \(R_1\). The manifold \(M\) is called Ric-semisymmetric if \(R(X,Y) \cdot R_1 = 0\). This paper's topic is the characterization of normally flat Ric-semisymmetric submanifolds in Euclidean spaces in terms of principal curvature vectors. Such a classification is know for normally flat Ric-semisymmetric hypersurfaces [\textit{V. A. Mirzoyan}, Sb. Math. 191, No. 9, 1323--1338 (2000); translation from Mat. Sb. 191, No. 9, 65--80 (2000; Zbl 1001.53006)]. In the non-hypersurface case, the situation is more complicated. The authors manage to characterize Einstein and semi-Einstein submanifolds and, as their central contribution, give a local geometric description for a certain class of submanifolds with co-dimension greater than one.
reviewed by: Hans-Peter Schröcker
Mathematics Subject Classification ID: 53B25
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53A07
zbMATH DE Number: 6148294
zbMATH Keywords: Ric-semisymmetric submanifold
zbMATH Keywords: Einstein submanifold
zbMATH Keywords: semi-Einstein submanifold
MaRDI profile type: Publication
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full work available at URL: s1066369x12090034
OpenAlex ID: W1997047014
description: scientific article; zbMATH DE number 6148294