KILLING VECTOR FIELDS OF CONSTANT LENGTH ON RIEMANNIAN NORMAL HOMOGENEOUS SPACES

Spaces of Conformal Vector Fields on Pseudo-riemannian Manifolds

We study Riemannian or pseudo-Riemannian manifolds which carry the space of closed conformal vector fields of at least 2-dimension. Subject to the condition that at each point the set of closed conformal vector fields spans a non-degenerate subspace of the tangent space at the point, we prove a global and a local classification theorems for such manifolds.

Concurrent vector fields on Finsler spaces

In this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α,β) -metric admits no concurrent vector fields. We also prove that an L-reducible Finsler metric admitting a concurrent vector field reduces to a Landsberg metric.In this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α,β) -metric admits no concurrent vector fi...

On Riemannian Curvature of Homogeneous Spaces

Harmonic-killing Vector Fields *

In this paper we consider the harmonicity of the 1-parameter group of local infinitesimal transformations associated to a vector field on a (pseudo-) Riemannian manifold to study this class of vector fields, which we call harmonic-Killing vector fields.

On the existence of Killing vector fields

In covariant metric theories of coupled gravity-matter systems the necessary and sufficient conditions ensuring the existence of a Killing vector field are investigated. It is shown that the symmetries of initial data sets are preserved by the evolution of hyperbolic systems.