A Characterization of the Infinitesimal Conformal Transformations on Tangent Bundles

a characterization of the infinitesimal conformal transformations on tangent bundles

On Infinitesimal Conformal Transformations of the Tangent Bundles with the Generalized Metric

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 ...

New structures on the tangent bundles and tangent sphere bundles

In this paper we study a Riemanian metric on the tangent bundle T (M) of a Riemannian manifold M which generalizes Sasaki metric and Cheeger Gromoll metric and a compatible almost complex structure which together with the metric confers to T (M) a structure of locally conformal almost Kählerian manifold. This is the natural generalization of the well known almost Kählerian structure on T (M). W...

A characterization of holonomy invariant functions on tangent bundles

We show that the holonomy invariance of a function on the tangent bundle of a manifold, together with very mild regularity conditions on the function, is equivalent to the existence of local parallelisms compatible with the function in a natural way. Thus, in particular, we obtain a characterization of generalized Berwald manifolds. We also construct a simple example of a generalized Berwald ma...

A Characterization of the Entropy--Gibbs Transformations

Let h be a finite dimensional complex Hilbert space, b(h)+ be the set of all positive semi-definite operators on h and Phi is a (not necessarily linear) unital map of B(H) + preserving the Entropy-Gibbs transformation. Then there exists either a unitary or an anti-unitary operator U on H such that Phi(A) = UAU* for any B(H) +. Thermodynamics, a branch of physics that is concerned with the study...

On the Topology of Tangent Bundles

is a vector space isomorphism of V" onto T(m). The tangent bundle 3(Af) of the manifold M consists of the ordered pairs (m, v) where mEM and vE T(m). Therefore, as a point set only, 3(Af) is M X V". We shall assume that the reader is familiar with the fibre space topology which is customarily assigned to 3(M). (For a description of this topology and the facts concerning fibre bundles which we s...