An extension of Rauch comparison theorem to glued Riemannian spaces
type: Item
instance of: scholarly article
title: An extension of Rauch comparison theorem to glued Riemannian spaces
zbMATH Open document ID: 1027.53035
author: Masakazu Takiguchi
published in: Tsukuba Journal of Mathematics
publication date: 2004-01-07T00:00:00Z
review text: Let \(B_i\) be submanifolds of Riemannian manifolds \(M_i\) for \(i=1,2\). One supposes that \(B_1\) and \(B_2\) are isometric and identifies \(M_1\) with \(M_2\) along the subspaces \(B_i\) to define a glued Riemannian space. A curve on such a space is said to be a \(B\) geodesic if it is a geodesic in each manifold separately and if it satisfies a certain passage law. The notion of a \(B\)-Jacobi vector field is defined similarly. The author generalizes the Rauch comparison theorem to this context; the shape operators of the submanifolds \(B_i\subset M_i\) play a crucial role in the analysis.
reviewed by: Peter B. Gilkey
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 1880967
zbMATH Keywords: Jacobi vector field
zbMATH Keywords: geodesics
zbMATH Keywords: shape operators
Wikidata QID: Q115233470
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496164428
OpenAlex ID: W1939517592
DOI: 10.21099/TKBJM/1496164428
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description: scientific article; zbMATH DE number 1880967