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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
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.

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

  • [1] C. Croke, Riemannian manifolds with large invariants, J. Differential Geom. 15 (1980), 467-491. MR 628339 (83a:53038)
  • [2] R. Greene and H. Wu, Function theory on manifolds which possess a pole, Lecture Notes in Math., vol. 699, Springer-Verlag, Berlin and New York, 1979. MR 521983 (81a:53002)
  • [3] S. Kobayashi and K. Nomizu, Foundations of differential geometry, vol. I, Interscience, New York, 1963. MR 0152974 (27:2945)
  • [4] F. Warner, Conjugate loci of constant order, Ann. of Math. (2) 86 (1967), 192-212. MR 0214005 (35:4857)

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Article copyright: © Copyright 1983 American Mathematical Society

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