2024-03-29T15:21:43Z
https://niigata-u.repo.nii.ac.jp/oai
oai:niigata-u.repo.nii.ac.jp:00002187
2022-12-15T03:34:59Z
176:488:489
453:454
Jacobi vector fields along geodesics in glued Riemannian manifolds
Jacobi vector fields along geodesics in glued Riemannian manifolds
Innami, Nobuhiro
7417
geodesic
Jacobi vector field
Rirmannian manifold
Let M_α, α∈∧, be complete connected Riemannian manifolds which are glued at their boundary. We call such a manifold M=U_<α∈∧>M_α a glued Rie-mannian manifold. Geodesics in a glued Riemannian manifold M are by definition locally minimizing curves in M. The variation vector fields through geodesics satisfy the Jacobi equation in each component manifold. In this paper we find the equation which show how Jacobi vector fields change in passing across the boundary of a com-ponent manifold into the neighboring component. As an application we characterize glued Riemannian manifolds whose glued boundary separates conjugate points.
journal article
新潟大学
2001
application/pdf
Nihonkai Mathematical Journal
1
12
101
112
Nihonkai Mathematical Journal
AA10800960
13419951
https://niigata-u.repo.nii.ac.jp/record/2187/files/5_0010.pdf
eng