Infinitesimal automorphisms on the tangent bundle

A Characterization of the Infinitesimal Conformal Transformations on Tangent Bundles

Multiplication on the Tangent Bundle

Manifolds with a commutative and associative multiplication on the tangent bundle are called F-manifolds if a unit field exists and the multiplication satisfies a natural integrability condition. They are studied here. They are closely related to discriminants and Lagrange maps. Frobenius manifolds are F-manifolds. As an application a conjecture of Dubrovin on Frobenius manifolds and Coxeter gr...

On Planar Webs with Infinitesimal Automorphisms

We investigate the space of abelian relations of planar webs admitting infinitesimal automorphisms. As an application we construct 4k − 14 new algebraic families of global exceptional k-webs on the projective plane, for each k ≥ 5.

Gromoll type metrics on the tangent bundle

In this paper we study a Riemanian metric on the tangent bundle T (M) of a Riemannian manifold M which generalizes the 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. We found conditions under which T (M) is almost Kählerian, locally conformal Kählerian or Kählerian or wh...

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 ...