We consider the unit tangent sphere bundle of Riemannian manifold ( M, g ) with g-natural metric G̃ and we equip it to an almost contact B-metric structure. Considering this structure, we show that there is a direct correlation between the Riemannian curvature tensor of ( M, g ) and local symmetry property of G̃. More precisely, we prove that the flatness of metric g is necessary and sufficien...

The objective of this paper is to explore the complete lifts a quarter-symmetric metric connection from Sasakian manifold its tangent bundle. A relationship between Riemannian and bundle was established. Some theorems on curvature tensor projective with respect were proved. Finally, locally ?-symmetric manifolds studied.

In the present paper, we have studied the properties of a quartersymmetric non-metric connection in an almost contact metric manifold.

This paper considers 4-dimensional manifolds upon which there is a Lorentz metric h and a symmetric connection Γ and which are originally assumed unrelated. It then derives sufficient conditions on h and Γ (expressed through the curvature tensor of Γ) for Γ to be the Levi-Civita connection of some (local) Lorentz metric g and calculates the relationship between g and h. Some examples are provid...

For any triple (M, g,∇) consisting of a Riemannian manifold and a metric connection with skew-symmetric torsion we introduce an elliptic, second order operator Ω acting on spinor fields. In case of a naturally reductive space and its canonical connection, our construction yields the Casimir operator of the isometry group. Several non-homogeneous geometries (Sasakian, nearly Kähler, cocalibrated...

In the present paper, we discuss singular minimal surfaces in Euclidean $3-$space $\mathbb{R}^{3}$ which are minimal. Such a surface is nothing but plane, trivial outcome. However, non-trivial outcome obtained when modify usual condition of minimality by using special semi-symmetric metric connection instead Levi-Civita on $\mathbb{R}^{3}$. With this new connection, prove that, besides planes, ...

Pseudo Ricci symmetric real hypersurfaces of a complex projective space are classified and it is proved that there are no pseudo Ricci symmetric real hypersurfaces of the complex projective space CPn for which the vector field ξ from the almost contact metric structure (φ, ξ, η, g) is a principal curvature vector field.