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RESEARCH PRODUCT
A topological obstruction to the geodesibility of a foliation of odd dimension
David L. JohnsonA. M. Naveirasubject
Differential geometrySimple (abstract algebra)Hyperbolic geometrySubbundleDimension (graph theory)Mathematics::Differential GeometryGeometry and TopologyAlgebraic geometryRiemannian manifoldTopologyMathematics::Symplectic GeometryFoliationMathematicsdescription
Let M be a compact Riemannian manifold of dimension n, and let ℱ 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 ℱ is totally geodesic. In this case, necessarily that portion of the Pontryagin algebra of the subbundle ℱ must vanish in degree n if ℱ is odd-dimensional. Using the same methods simple proofs of the theorems of Bott and Pasternack are given.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1981-09-01 | Geometriae Dedicata |