We consider the unit tangent sphere bundle of Riemannian manifold ( M, g ) with g-natural metric G̃ and we equip it to an almost contact B-metric structure. Considering this structure, we show that there is a direct correlation between the Riemannian curvature tensor of ( M, g ) and local symmetry property of G̃. More precisely, we prove that the flatness of metric g is necessary and sufficien...

Let  be an n-dimensional Riemannian manifold, and  be its tangent bundle with the lift metric. Then every infinitesimal fiber-preserving conformal transformation  induces an infinitesimal homothetic transformation on .  Furthermore,  the correspondence   gives a homomorphism of the Lie algebra of infinitesimal fiber-preserving conformal transformations on  onto the Lie algebra of infinitesimal ...

Let X be a Fano manifold with Picard number one such that the tangent bundle $${{T}_{X}}$$ is big. If admits rational curve trivial normal bundle, we show isomorphic to del Pezzo threefold of degree five.

A tangent Lie group with elements and group operations which are tangent prolongations of those corresponding to another Lie group is examined. An action of such extended Lie group on differentiable manifold and its tangent bundle is defined by using contact transformations. It turned out that a tangent Lie symmetrical Lagrangian describes a dynamical system with first-class constraints. Geomet...

Lagrange geometry is the geometry of the tensor field defined by the fiberwise Hessian of a non degenerate Lagrangian function on the total space of a tangent bundle. Finsler geometry is the geometrically most interesting case of Lagrange geometry. In this paper, we study a generalization, which consists of replacing the tangent bundle by a general tangent manifold, and the Lagrangian by a fami...

Visual curve completion is a fundamental perceptual mechanism that completes the missing parts (e.g., due to occlusion) between observed contour fragments, and facilitates higher level vision. Recent computational, neurophysiological, and psychophysical studies suggest that completed curves emerge from activation patterns of orientation selective cells in the primary visual cortex, as if they w...

In this paper, we develop the theory of singular hermitian metrics on vector bundles. As an application, give a structure theorem projective manifold $X$ with pseudo-effective tangent bundle: admits smooth fibration $X \to Y$ to flat $Y$ such that its general fiber is rationally connected. Moreover, by applying theorem, classify all minimal surfaces bundle and study non-minimal surfaces, which ...