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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
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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?)

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  • [2] John Bolton, The Morse Index Theorem in the case of two variable end-points, J. Differential Geom. 12 (1977), 567-581. MR 512926 (80b:58025)
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  • [4] J. Milnor, Morse theory, Ann. of Math. Studies, no. 51, Princeton Univ. Press, Princeton, N.J., 1973. MR 0163331 (29:634)

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

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