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Transactions of the American Mathematical Society

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

 

 

Decomposition theorems of Riemannian manifolds


Author: Pyng Wang
Journal: Trans. Amer. Math. Soc. 184 (1973), 327-341
MSC: Primary 53C20
DOI: https://doi.org/10.1090/S0002-9947-1973-0328824-8
MathSciNet review: 0328824
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Abstract: Given two complementary orthogonal parallel foliations on a complete connected Riemannian manifold M, a necessary and sufficient condition for the direct product of the two leaves through a point m being a covering manifold of M is obtained. It is shown that the direct product of the two leaves through m of the two foliations is a Riemannian covering of M if the two leaves are regular at m. Moreover, if one of the foliations is regular and the intersection of the two leaves through m contains only the point m, then M is isometric to the direct product of the two leaves.


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DOI: https://doi.org/10.1090/S0002-9947-1973-0328824-8
Article copyright: © Copyright 1973 American Mathematical Society