Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

The Morse index theorem where the ends are submanifolds


Author: Diane Kalish
Journal: Trans. Amer. Math. Soc. 308 (1988), 341-348
MSC: Primary 58E10
DOI: https://doi.org/10.1090/S0002-9947-1988-0946447-5
MathSciNet review: 946447
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper the Morse Index Theorem is proven in the case where submanifolds $ P$ and $ Q$ are at the endpoints of a geodesic, $ \gamma $. At $ \gamma $, the index of the Hessian of the energy function defined on paths joining $ P$ and $ Q$ is computed using $ P$-focal points, and a calculation at the endpoint of $ \gamma $, involving the second fundamental form of $ Q$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 58E10

Retrieve articles in all journals with MSC: 58E10


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1988-0946447-5
Article copyright: © Copyright 1988 American Mathematical Society