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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Compactness criteria for Riemannian manifolds


Author: Gregory J. Galloway
Journal: Proc. Amer. Math. Soc. 84 (1982), 106-110
MSC: Primary 53C20
DOI: https://doi.org/10.1090/S0002-9939-1982-0633289-3
MathSciNet review: 633289
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Abstract: Ambrose, Calabi and others have obtained Ricci curvature conditions (weaker than Myers' condition) which ensure the compactness of a complete Riemannian manifold. Using standard index form techniques we relate the problem of finding such Ricci curvature criteria to that of establishing the conjugacy of the scalar Jacobi equation. Using this relationship we obtain a Ricci curvature condition for compactness which is weaker than that of Ambrose and, in fact, which is best among a certain class of conditions.


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DOI: https://doi.org/10.1090/S0002-9939-1982-0633289-3
Article copyright: © Copyright 1982 American Mathematical Society