Decomposition theorems of Riemannian manifolds
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- by Pyng Wang PDF
- Trans. Amer. Math. Soc. 184 (1973), 327-341 Request permission
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.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- 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