Remarks on Chen's inequalities for submanifolds of a Riemannian manifold of nearly quasi-constant curvature
type: Item
instance of: scholarly article
title: Remarks on Chen's inequalities for submanifolds of a Riemannian manifold of nearly quasi-constant curvature
zbMATH Open document ID: 1337.53075
author: Pan Zhang
published in: Vietnam Journal of Mathematics
publication date: 2015-09-22T00:00:00Z
review text: This paper concerns Chen's inequalities for submanifolds of Riemannian spaces of nearly quasi-constant curvature. A main result is an inequality between the Ricci curvature and the squared mean curvature of the submanifold obtained using an algebraic lemma. The class of warped product submanifolds is intensively studied.
reviewed by: Constantin Călin
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53B05
Mathematics Subject Classification ID: 53B15
zbMATH DE Number: 6484012
zbMATH Keywords: Chen's inequalities
zbMATH Keywords: Chen-Ricci inequalities
zbMATH Keywords: warped product
zbMATH Keywords: nearly quasi-constant curvature
MaRDI profile type: Publication
full work available at URL: s10013-014-0096-9
OpenAlex ID: W2142603060
cites work: Certain inequalities for submanifolds in \((K,\mu)\)-contact space forms
cites work: Manifolds of Negative Curvature
cites work: Mean curvature and shape operator of isometric immersions in real-space-forms
cites work: Totally real submanifolds of \(\mathbb{C} P^ n\) satisfying a basic equality
cites work: A tour through δ-invariants: From Nash’s embedding theorem to ideal immersions, best ways of living and beyond
cites work: Some pinching and classification theorems for minimal submanifolds
cites work: A Riemannian invariant and its applications to submanifold theory
cites work: Ideal Lagrangian immersions in complex space forms
cites work: Optimal general inequalities for Lagrangian submanifolds in complex space forms
cites work: Q3070798
cites work: Classification of Lagrangian submanifolds in complex space forms satisfying a basic equality involving \(\delta(2,2)\)
cites work: Q5673532
cites work: Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimensions
cites work: ON ISOMETRIC MINIMAL IMMERSIONS FROM WARPED PRODUCTS INTO REAL SPACE FORMS
cites work: Non-immersion theorems for warped products in complex hyperbolic spaces
cites work: A general optimal inequality for warped products in complex projective spaces and its applications.
cites work: Geometry of \(\mathcal P R\)-warped products in para-Kähler manifolds
cites work: Q4670335
cites work: Chen inequalities for submanifolds of real space forms with a semi-symmetric metric connection
cites work: Q3070705
cites work: Q3070657
cites work: Proregular sequences, local cohomology, and completion
cites work: Contact CR-warped product submanifolds in Sasakian manifolds
cites work: Q5475655
cites work: Ricci curvature of submanifolds in Sasakian space forms
cites work: The imbedding problem for Riemannian manifolds
cites work: Chen's inequality in the Lagrangian case
cites work: Q3098566
cites work: Q3149323
cites work: Chen inequalities for submanifolds of a Riemannian manifold of nearly quasi-constant curvature
cites work: Convergence properties of projection and contraction methods for variational inequality problems
cites work: Q5306683
Wikidata QID: Q115385462
DOI: 10.1007/S10013-014-0096-9
description: scientific article; zbMATH DE number 6484012