Avijit Sarkar

Some curvature properties of trans-Sasakian manifolds

The object of the present paper is to study quasi-conformally flat trans-Sasakian manifolds. We consider trans-Sasakian manifolds with η-parallel and cyclic parallel Ricci tensors. ϕ-Ricci symmetric quasi-conformally flat trans-Sasakian manifolds have been studied. We also investigates quasi-conformally flat trans-Sasakian manifolds which are Einstein Semi-symmetric.

SOME CURVES ASSOCIATED WITH α-SASAKIAN MANIFOLDS

The aim of the present paper is to study biharmonic magnetic curves on three-dimensional a-Sasakian manifolds. We also characterize biminimal curves on a hypersurface of a three-dimensional a-Sasakian manifold with constant curvature.

A study on Legendre curves in 3-dimensional trans-Sasakian manifolds

The object of the present paper is to show that Theorem 3 of the paper [22] on 3-dimensional quasi-Sasakianmanifolds can be extended to 3-dimensional trans-Sasakian manifolds. We also find the curvature and torsion of Legendre curves in 3-dimensional trans-Sasakian manifolds with respect to semisymmetric metric connection. Keywords and phrases: Legendre curve, trans-Sasakian manifold, semisymmetric metric connection, curvature, torsion.

Generalized Sasakian-Space-Forms with Projective Curvature Tensor

Abstract The object of the present paper is to study Ф-projectively flat generalized Sasakian-space-forms, projectively locally symmetric generalized Sasakian-space-forms and projectively locally Ф-symmetric generalized Sasakian-space-forms. All the obtained results are in the form of necessary and sufficient conditions. Interesting relations between projective curvature tensor and conformal curvature tensor of a generalized Sasakian-spaceform of dimension greater than three have been established. Some of these properties are also analyzed in the light of quarter-symmetric metric connection, in addition with the Levi-Civita connection. Obtained results are supported by illustrative examples.