In the first part of this paper, some theorems are given for a Riemannian manifold with semi-symmetric metric connection. In the second part of it, some special vector fields, for example, torse-forming vector fields, recurrent vector fields and concurrent vector fields are examined in this manifold. We obtain some properties of this manifold having the vectors mentioned above.

in this study, 2n -dimensional (n > 2) generalized conformally recurrent kaehlerian weyl spaces andgeneralized conharmonicaly recurrent kaehlerian weyl spaces are defined. it is proved that a kaehlerian weylspace is generalized conformally recurrent if and only if it is generalized recurrent.also, it is shown that akaehlerian weyl space will be generalized recurrent if and only if it is general...

We apply mirror symmetry to the super Calabi-Yau manifold CP and show that the mirror can be recast in a form which depends only on the superdimension and which is reminiscent of a generalized conifold. We discuss its geometrical properties in comparison to the familiar conifold geometry. In the second part of the paper examples of special-Lagrangian submanifolds are constructed for a class of ...

The object of the present paper is to study the extended generalized φ-recurrent trans-Sasakian manifold and its various geometric properties.

We extend the notion of generalized φ-recurrent β-Kenmotsu manifold and study its various geometric properties with the existence of such notion.

In this paper we develope the fundamentals of the generalized symplectic geometry on the bundle of linear frames LM of an n-dimensional manifold M that follows upon taking the R-valued soldering 1-form θ on LM as a generalized symplectic potential. The development is centered around generalizations of the basic structure equation df = −Xf ω of standard symplectic geometry to LM when the symplec...

Conformally flat pseudo-Riemannian manifolds with generalized Ricci recurrent, $(GR)_n$ structure are completely classified in this short report. A conformally recurrent manifold is shown to be either a de Sitter space or an anti-de space. In particular, spacetime must spacetime.

The object of the present paper is to study semi-symmetric metric connection on a 3-dimensional trans-Sasakian manifold. We found necessary condition under which vector field manifold will be strict contact field. Then, we obtained extended generalized phi-recurrent with respect connection. Next, satises ~L.~ S = 0 studied.

The object of the present paper is to introduce a non-flat Riemannian manifold called hyper-generalized recurrent manifolds and study its various geometric properties along with the existence of a proper example.

The object of this paper is to study invariant submanifolds M of Kenmotsu manifolds M̃ admitting a quarter symmetric metric connection and to show that M admits quarter symmetric metric connection. Further it is proved that the second fundamental forms σ and σ with respect to LeviCivita connection and quarter symmetric metric connection coincide. Also it is shown that if the second fundamental f...