Generalized Chen submanifolds
type: Item
instance of: scholarly article
title: Generalized Chen submanifolds
zbMATH Open document ID: 0794.53035
DOI: 10.1007/BF01226805
published in: Journal of Geometry
publication date: 1994-01-31T00:00:00Z
review text: Generalized Chen submanifolds or \(k\)-th Chen submanifolds are defined. The authors give a characterization of those submanifolds in terms of an operator of J. Simons. They relate these submanifolds to submanifolds of finite type introduced by B. Y. Chen and prove that: Let \(M\) be a compact submanifold in \(E^ m\) with parallel second fundamental form; then \(M\) is of finite \(k\)-type if and only if \(M\) is a \(k\)-th Chen submanifold in \(E^ m\).
reviewed by: Thomas Hasanis
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53B25
zbMATH DE Number: 493208
zbMATH Keywords: Chen submanifolds
zbMATH Keywords: finite type
zbMATH Keywords: parallel second fundamental form
author: Shijie Li
author: C. S. Houh
MaRDI profile type: Publication
cites work: Pseudo-umbilical submanifolds of a Riemannian manifold of constant curvature . II
cites work: Q3314490
cites work: Q3322795
cites work: Q3740594
cites work: Q3672666
cites work: Characterization and examples of Chen submanifolds
cites work: Q4137728
cites work: Minimal varieties in Riemannian manifolds
full work available at URL: https://doi.org/10.1007/bf01226805
OpenAlex ID: W1977775942
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description: scientific article; zbMATH DE number 493208