Submanifolds with parallel Ricci tensor
type: Item
instance of: scholarly article
title: Submanifolds with parallel Ricci tensor
zbMATH Open document ID: 0656.53054
author: Yoshio Matsuyama
published in: Kodai Mathematical Journal
publication date: 1988-01-01T00:00:00Z
review text: The author gives a classification of submanifolds of a Riemannian manifold of constant sectional curvature having parallel Ricci tensor, parallel mean curvature vector field and trivial normal connection. A corollary is the classification of 2-codimensional Einstein submanifolds of a Riemannian manifold of constant sectional curvature having parallel mean curvature vector field. It is shown that the submanifolds in question have parallel second fundamental form. The proof of Theorem 1 as it is written in the paper seems to be incomplete but the lacking arguments can be supplied rather easily.
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 4071848
zbMATH Keywords: parallel Ricci tensor
zbMATH Keywords: parallel mean curvature vector
zbMATH Keywords: normal connection
zbMATH Keywords: Einstein submanifolds
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138038876
OpenAlex ID: W2010480506
Wikidata QID: Q124853079
cites work: Q3756079
cites work: Isometric Immersions of Constant Mean Curvature and Triviality of the Normal Connection
cites work: Q4439341
cites work: Hypersurfaces with parallel Ricci tensor
cites work: Q3937990
cites work: Submanifolds with parallel mean curvature vector
DOI: 10.2996/KMJ/1138038876
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description: scientific article; zbMATH DE number 4071848