A topological obstruction to the geodesibility of a foliation of odd dimension |
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Authors: | David L Johnson A M Naveira |
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Institution: | (1) Department of Mathematics, Texas A & M University, 77843 College Station, Texas, USA;(2) Departamento de Geometria y Topologia Facultad de Ciencias Matemáticas, Universidad de Valencia, Valencia, Spain |
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Abstract: | Let M be a compact Riemannian manifold of dimension n, and let be a smooth foliation on M. A topological obstruction is obtained, similar to results of R. Bott and J. Pasternack, to the existence of a metric on M for which is totally geodesic. In this case, necessarily that portion of the Pontryagin algebra of the subbundle must vanish in degree n if is odd-dimensional. Using the same methods simple proofs of the theorems of Bott and Pasternack are given. |
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Keywords: | Primary 57D30 Secondary 53B25 53C20 |
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