Remote Access Transactions of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 53C21, 53C25

Retrieve articles in all journals with MSC: 53C21, 53C25


Additional Information

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

American Mathematical Society