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The present paper deals the study of generalised Sasakian-space-forms with the conditions Cq(ξ,X).S = 0, Cq(ξ,X).R = 0 and Cq(ξ,X).Cq = 0, where R, S and Cq denote Riemannian curvature tensor, Ricci tensor and quasi-conformal curvature tensor of the space-form, respectively and at last, we have given some examples to improve our results.

The present paper deals the study of a Bochner Ricci pseudosymmetric super quasi-Einstein Hermitian manifold and a holomorphically projective Ricci pseudo-symmetric super quasi-Einstein Hermitian manifold.

In this paper, we have studied a conformal transformation between two almost Hermitian manifolds and shown that the associated Nijenhuis tensor is conformally invariant under this transformation. We have also discussed the properties of contravariant almost analytic vector field, covariant almost analytic vector field and some other properties in almost Hermitian manifold under this transformation.

In this paper, a new type of generalized quasi-Einstein manifold is defined. The special cases of this manifold are Einstein manifold, quasi-Einstein manifold and nearly quasi-Einstein manifold. We have shown the existence of this new type of generalised quasi-Einstein manifold by a suitable example.