On some Riemannian manifolds admitting a metric semi-symmetric connection
In this paper we present a review of recent results on semi-Riemannian manifolds satisfying curvature conditions of pseudosymmetry type.
We study slant curves in contact Riemannian 3-manifolds with pseudo-Hermitian proper mean curvature vector field and pseudo-Hermitian harmonic mean curvature vector field for the Tanaka-Webster connection in the tangent and normal bundles, respectively. We also study slant curves of pseudo-Hermitian AW(k)-type.
N. S. Sinyukov [5] introduced the concept of an almost geodesic mapping of a space with an affine connection without torsion onto and found three types: , and . The authors of [1] proved completness of that classification for .By definition, special types of mappings are characterized by equations where is the deformation tensor of affine connections of the spaces and .In this paper geometric objects which preserve these mappings are found and also closed classes of such spaces...
Using a general connection Γ on a fibred manifold p:Y → M and a torsion free classical linear connection ∇ on M, we distinguish some “special” fibred coordinate systems on Y, and then we construct a general connection on Fp:FY → FM for any vector bundle functor F: ℳ f → of finite order.
The paper deals with tensor fields which are semiconjugated with torse-forming vector fields. The existence results for semitorse-forming vector fields and for convergent vector fields are proved.