A complete noncompact manifold M with nonnegative sectional curvature is diffeomorphic to the normal bundle of a compact submanifold S called the soul of M . When S is a round sphere we show that the clutching map of this bundle is restricted; this is used to deduce that there are at most finitely many isomorphism types of such bundles with sectional curvature lying in a fixed interval [0, κ]. ...

In [6], the geometric dimension of all stable vector bundles over real projective space P was determined if n is even and sufficiently large with respect to the order 2 of the bundle in K̃O(P). Here we perform a similar determination when n is odd and e > 6. The work is more delicate since P does not admit a v1-map when n is odd. There are a few extreme cases which we are unable to settle precis...

This work is divided in two cases. In the first case, we consider a spin manifold M as set of fixed points an S1-action on X, and second case loop space M. For each build vector bundle, connection bundle endomorphisms. These objects are used to global operators which define analytical index case. equal topological equivariant Atiyah–Singer index, expression where Witten genus appears.

A generalized Courant algebroid structure is defined on the direct sum bundle DE ⊕ JE, where DE and JE are the gauge Lie algebroid and the jet bundle of a vector bundle E respectively. Such a structure is called an omni-Lie algebroid since it is reduced to the omni-Lie algebra introduced by A.Weinstein if the base manifold is a point. We prove that any Lie algebroid structure on E is characteri...

fibre is the re-dimensional complex projective space (complex projective co-tangent bundle). This bundle of complex dimension 2re + l is our M. Considering the fibre of T(V) as the (2w+2)-dimensional real vector space, we take as P the co-tangent sphere bundle over V (i.e., the fibre of P is a sphere in the fibre of T(V)). T(V) — V is the principal fibre bundle associated with a line bundle L o...

In this article, we present some results concerning the harmonicity on tangent bundle equipped with vertical rescaled metric. We establish necessary and sufficient conditions under which a vector field is harmonic respect to metric construct examples of fields. also study along map between Riemannian manifolds, target manifold its bundle. Next discuss composition projection from into another ma...