Let (M,1) be a Riemannian manifold and T2M its second order tangent bundle. In this paper, we deal with certain characterizations of F?geodesics (which generalize both classical geodesics magnetic curves) on the bundle hypersurface T21,1M respect to some natural metrics.

The purpose of the present work is to study behavior cross-section metallic structure in M tangent bundle TM.

We define a subcategory of the category of diffeological spaces, which contains smooth manifolds, the diffeomorphism subgroups and its coadjoint orbits. In these spaces we construct a tangent bundle, vector fields and a de Rham cohomology.

Let X be a Fano variety of Picard number one defined over an algebraically closed field. We give conditions under which the tangent bundle of a complete intersection on X is stable or strongly stable.

The objective of this paper is to explore the complete lifts a quarter-symmetric metric connection from Sasakian manifold its tangent bundle. A relationship between Riemannian and bundle was established. Some theorems on curvature tensor projective with respect were proved. Finally, locally ?-symmetric manifolds studied.

We produce new examples of harmonic maps, having as either source or target manifold the tangent bundle TM on a Riemannian manifold (M,g), equipped with a Riemannian g-natural metric G. In particular, we study the harmonicity of the canonical projection π : (TM,G)→ (M,g), and of the identity map (TM,G)→ (TM,gS) and conversely, gS being the Sasaki metric on TM. A corresponding study is made for ...

given a pair (semispray $s$, metric $g$) on a tangent bundle, the family of nonlinear connections $n$ such that $g$ is recurrent with respect to $(s, n)$ with a fixed recurrent factor is determined by using the obata tensors. in particular, we obtain a characterization for a pair $(n, g)$ to be recurrent as well as for the triple $(s, stackrel{c}{n}, g)$ where $stackrel{c}{n}$ is the canonical ...

The anisotropic blowup along the zero section and the fiberwise compactification of a real vector bundle F → X are manifolds with boundary for which the natural structure bundle is the b-tangent bundle. We give a necessary and sufficient condition for these procedures to give a b-complex structure when applied to a holomorphic vector bundle over a complex manifold, and analyze some aspects of t...

The contact geometric structure of the thermodynamic phase space is used to introduce a novel symplectic on tangent bundle equilibrium space. Moreover, it turns out that can be interpreted as Lagrange submanifold corresponding bundle, if fundamental equation known explicitly. As consequence, Hamiltonians defined describe processes.