A Morse index theorem for geodesics on a glued Riemannian space

Kodai Mathematical Journal

Masakazu Takiguchi¹ 

关键词: Entire Function;    Meromorphic function;    Share value;    Unicity;   

DOI  :  10.2996/kmj/1104247352

学科分类：数学（综合）

来源: Tokyo Institute of Technology, Department of Mathematics

【 摘 要 】

References(11)A glued Riemannian space is obtained from Riemannian manifolds M1 and M2 by identifying their isometric submanifolds B1 and B2. A curve on a glued Riemannian space which is a geodesic on each Riemannian manifold and satisfies certain passage law on the identified submanifold B := B1 ≅ B2 is called a B-geodesic. Considering the variational problem with respect to arclength L of piecewise smooth curves through B, a critical point of L is a B-geodesic. A B-Jacobi field is a Jacobi field on each Riemannian manifold and satisfies certain passage condition on B. In this paper, we extend the Morse index theorem for geodesics in Riemannian manifolds to the case of a glued Riemannian space.

【 授权许可】

Unknown