The S-curvature of homogeneous Randers spaces

Vanishing S-curvature of Randers spaces

We give a necessary and sufficient condition on a Randers space for the existence of a measure for which Shen’s S-curvature vanishes everywhere. Moreover, such a measure coincides with the Busemann-Hausdorff measure up to a constant multiplication.

On 5-dimensional 2-step homogeneous randers nilmanifolds of Douglas type

‎In this paper we first obtain the non-Riemannian Randers metrics of Douglas type on two-step homogeneous nilmanifolds of dimension five‎. ‎Then we explicitly give the flag curvature formulae and the $S$-curvature formulae for the Randers metrics of Douglas type on these spaces‎. ‎Moreover‎, ‎we prove that the only simply connected five-dimensional two-step homogeneous Randers nilmanifolds of D...

On Riemannian Curvature of Homogeneous Spaces

Curvature homogeneous spaces whose curvature tensors have large symmetries

We study curvature homogeneous spaces or locally homogeneous spaces whose curvature tensors are invariant by the action of “large” Lie subalgebras h of so(n). In this paper we deal with the cases of h = so(r)⊕ so(n− r) (2 ≤ r ≤ n− r), so(n− 2), and the Lie algebras of Lie groups acting transitively on spheres, and classify such curvature homogeneous spaces or locally homogeneous spaces.

Some Examples of Randers Spaces

A Riemannian almost product structure on a manifold induces on a submanifold of codimension 1 a structure generalizing the paracontact structures and containing a Riemannain metric and an one form . We show that the pair consisting of this Riemannian metric and one form defines a strongly convex Randers metric on submanifold. We establish some properties of this Randers metric and we provide so...