30 research outputs found
On harmonic vector fields
A tangent bundle to a Riemannian manifold carries various metrics induced by a Riemannian tensor. We consider harmonic vector fields with respect to some of these metrics . We give a simple proof that a vector field on a compact manifold is harmonic with respect to the Sasaki metric on TM if and only if it is parallel. We also consider the metrics II and I + II on a tangent bundle (cf. [YI]) and harmonic vector fields generated by them
A Darboux theorem for generalized contact manifolds
We consider a manifold M equipped with 1-forms which satisfy certain contact like properties. We prove a generalization of the classical Darboux theorem for such manifolds
A Darboux theorem for generalized contact manifolds
We consider a manifold M equipped with 1-forms which satisfy certain contact like properties. We prove a generalization of the classical Darboux theorem for such manifolds
Natural Diagonal Riemannian Almost Product and Para-Hermitian Cotangent Bundles
We obtain the natural diagonal almost product and locally product structures
on the total space of the cotangent bundle of a Riemannian manifold. We find
the Riemannian almost product (locally product) and the (almost) para-Hermitian
cotangent bundles of natural diagonal lift type. We prove the characterization
theorem for the natural diagonal (almost) para-K\"ahlerian structures on the
total spaces of the cotangent bundle.Comment: 10 pages, will appear in Czechoslovak Mathematical Journa
On harmonic vector fields
A tangent bundle to a Riemannian manifold carries various metrics induced by a Riemannian tensor. We consider harmonic vector fields with respect to some of these metrics . We give a simple proof that a vector field on a compact manifold is harmonic with respect to the Sasaki metric on TM if and only if it is parallel. We also consider the metrics II and I + II on a tangent bundle (cf. [YI]) and harmonic vector fields generated by them