The object of the present paper is to study the nature of generalized Sasakian-space-forms under some conditions regarding projective curvature tensor. All the results obtained in this paper are in the form of necessary and sufficient conditions.

The object of the present paper is to study generalized Sasakian-space-forms with vanishing quasi-conformal curvature tensor. The space-forms satisfying ▿S = 0 and R.S = 0 are also considered.

The object of the present paper is to find necessary and sufficient conditions for invariant submanifolds of trans-Sasakian manifolds to be totally geodesic. As a remark, particular cases of submanifolds of α-Sasakian and β-Kenmotsu manifolds are considered and the difference between the conditions for submanifolds of α-Sasakian and β-Kenmotsu manifolds to be totally geodesic is shown.

The object of the present paper is to study pseudo-slant submanifolds of trans-Sasakian manifolds. Integrability conditions of the distributions on these submanifolds are worked out. Some interesting results regarding such manifolds have also been deduced. An example of a pseudo-slant submanifold of a trans-Sasakian manifold is given.

The aim of the present article is to analyze three-dimensional quasi-Sasakian manifolds admitting Riemann solitons and Ricci Bourguignon solitons.