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A topological obstruction to the geodesibility of a foliation of odd dimension

✍ Scribed by David L. Johnson; A. M. Naveira

Publisher
Springer
Year
1981
Tongue
English
Weight
292 KB
Volume
11
Category
Article
ISSN
0046-5755

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✦ Synopsis

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 .N is odd-dimensional. Using the same methods simple proofs of the theorems of Bott and Pasternack are given.

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