A Morse index theorem for geodesics on a glued Riemannian space
type: Item
instance of: scholarly article
title: A Morse index theorem for geodesics on a glued Riemannian space
zbMATH Open document ID: 1085.53032
author: Masakazu Takiguchi
published in: Kodai Mathematical Journal
publication date: 2005-04-18T00:00:00Z
review text: A glued Riemannian space is obtained from Riemannian manifolds \(M_1\) and \(M_2\), by identifyng some isometric submanifolds \(B_1\) and \(B_2\). (In general, it is not a smooth Riemannian manifold, and equality of dimensions is not required.) A \(B\)-geodesic in a glued Riemannian space is a geodesic on \(M_1\) and \(M_2\) respectively, such that it has the same projected velocity in \(TB_1=TB_2\), and assume the same value on the respective metric tensors at its points in \(B_1=B_2\). The notion of Jacobi fields, conjugated points, and Morse index are studied for these \(B\)-geodesics.
reviewed by: Jesus Muciño Raymundo
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 53B20
zbMATH DE Number: 2157861
zbMATH Keywords: geodesics
zbMATH Keywords: Morse index
zbMATH Keywords: glued Riemannian space
MaRDI profile type: Publication
OpenAlex ID: W1994654824
Wikidata QID: Q115224665
DOI: 10.2996/KMJ/1104247352
description: scientific article; zbMATH DE number 2157861