A comparison-estimate of the second Rauch type for Ricci curvature
type: Item
instance of: scholarly article
title: A comparison-estimate of the second Rauch type for Ricci curvature
zbMATH Open document ID: 1118.53019
author: Zisheng Hu
author: Senlin Xu
published in: Geometriae Dedicata
publication date: 2007-06-07T00:00:00Z
review text: Rauch's comparison theorem in Riemannian geometry is concerned with sectional curvature. For the Ricci tensor, a comparison-estimate of the first Rauch type has been established by \textit{C. Dai} and \textit{S. Wei} [Math. Ann. 303, No. 2, 297--306 (1995; Zbl 0834.53035)]. In this paper, the authors establish a comparison-estimate of the second Rauch type for Ricci curvature. As an application, they obtain a result of local splitting for Riemannian manifolds.
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C22
zbMATH DE Number: 5162125
zbMATH Keywords: Ricci curvature
zbMATH Keywords: Jacobi field
zbMATH Keywords: geodesic hypersurface
zbMATH Keywords: local splitting
reviewed by: Nabil L. Youssef
MaRDI profile type: Publication
full work available at URL: s10711-006-9121-9
OpenAlex ID: W2133827831
cites work: \(C^ \alpha\)-compactness for manifolds with Ricci curvature and injectivity radius bounded below
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cites work: Q4287762
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cites work: The splitting theorem for manifolds of nonnegative Ricci curvature
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cites work: Negative Ricci curvature and isometry group
cites work: A comparison-estimate of Toponogov type for Ricci curvature
cites work: A contribution to differential geometry in the large
cites work: Extension of the Rauch Comparison Theorem to Submanifolds
cites work: Q4370148
DOI: 10.1007/S10711-006-9121-9
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description: scientific article; zbMATH DE number 5162125