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Transactions of the American Mathematical Society

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

 

 

On the integrability of Jacobi fields on minimal submanifolds


Author: D. S. P. Leung
Journal: Trans. Amer. Math. Soc. 220 (1976), 185-194
MSC: Primary 53B25; Secondary 49F10, 35J50
MathSciNet review: 0405269
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Abstract: Let M be a minimal submanifold of a Riemannian manifold. It is proved that every Jacobi field on M is locally the deformation vector field along M of some one-parameter families of minimal submanifolds. This fact follows from a theorem on nonlinear elliptic systems which is also proved in this paper. The related global problems are also discussed briefly.


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DOI: https://doi.org/10.1090/S0002-9947-1976-0405269-6
Keywords: Strongly elliptic system, minimal submanifold, Jacobi field
Article copyright: © Copyright 1976 American Mathematical Society