The Tangent Space at a Special Symplectic Instanton Bundle on IP

The Tangent Space at a Special Symplectic Instanton Bundle on IP2n+1

Tangent Bundle of the Hypersurfaces in a Euclidean Space

Let $M$ be an orientable hypersurface in the Euclidean space $R^{2n}$ with induced metric $g$ and $TM$ be its tangent bundle. It is known that the tangent bundle $TM$ has induced metric $overline{g}$ as submanifold of the Euclidean space $R^{4n}$ which is not a natural metric in the sense that the submersion $pi :(TM,overline{g})rightarrow (M,g)$ is not the Riemannian submersion. In this paper...

Identification of Riemannian foliations on the tangent bundle via SODE structure

The geometry of a system of second order differential equations is the geometry of a semispray, which is a globally defined vector field on TM. The metrizability of a given semispray is of special importance. In this paper, the metric associated with the semispray S is applied in order to study some types of foliations on the tangent bundle which are compatible with SODE structure. Indeed, suff...

On the k-nullity foliations in Finsler geometry

Here, a Finsler manifold $(M,F)$ is considered with corresponding curvature tensor, regarded as $2$-forms on the bundle of non-zero tangent vectors. Certain subspaces of the tangent spaces of $M$ determined by the curvature are introduced and called $k$-nullity foliations of the curvature operator. It is shown that if the dimension of foliation is constant, then the distribution is involutive...

The Tangent Bundle of an Almost-complex Free Loopspace

The space LV of free loops on a manifold V inherits an action of the circle group T. When V has an almost-complex structure, the tangent bundle of the free loopspace, pulled back to a certain infinite cyclic cover g LV , has an equivariant decomposition as a completion of TV ⊗ (⊕C(k)), where TV is an equivariant bundle on the cover, nonequivariantly isomorphic to the pullback of TV along evalua...