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Transactions of the American Mathematical Society

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

 

 

Characterizations of simply connected rotationally symmetric manifolds


Author: Hyeong In Choi
Journal: Trans. Amer. Math. Soc. 275 (1983), 723-727
MSC: Primary 53C21; Secondary 53C25
DOI: https://doi.org/10.1090/S0002-9947-1983-0682727-4
MathSciNet review: 682727
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Abstract: We prove that a simply connected, complete Riemannian manifold $ M$ is rotationally symmetric at $ p$ if and only if the exponential image of every linear subspace of $ {M_p}$ is a smooth, closed, totally geodesic submanifold of $ M$. This result is in essence Schur's theorem at one point $ p$, as it becomes apparent in the proof.


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DOI: https://doi.org/10.1090/S0002-9947-1983-0682727-4
Article copyright: © Copyright 1983 American Mathematical Society