Some results on the properties of T -flat, quasiT -flat,  T -flat,  T -flat, T -semi-symmetric,  T Ricci recurrent and T - -recurrent LP-Sasakian manifolds are obtained. It is also proved that an LP-Sasakian manifold satisfying the condition T . 0 S  is an  -Einstein manifold. MSC 2000. 53C15, 53C25, 53C50, 53D15.

The object of the present paper is to consider f-Kenmotsu 3-manifolds
 fulfilling certain curvature conditions on Q-curvature tensor with
 Schouten-van Kampen connection. Certain consequences Q-curvature
 such manifolds bearing Ricci soliton in perspective Schouten-van
 association are likewise displayed. In last segment, examples are
 given.

We define a generalized mass for asymptotically flat manifolds using some higher order symmetric function of the curvature tensor. This mass is nonnegative when the manifold is locally conformally flat and the σk curvature vanishes at infinity. In addition, with the above assumptions, if the mass is zero, then, near infinity, the manifold is isometric to a Euclidean end.

We study symplectic manifolds (M, ω) equipped with a symplectic torsion-free affine (also called Fedosov) connection ∇ and admitting a metaplectic structure. Let S be the so called symplectic spinor bundle and let R be the curvature tensor field of the symplectic spinor covariant derivative ∇ associated to the Fedosov connection ∇. It is known that the space of symplectic spinor valued exterior...

We compute the number of linearly independent ways in which a tensor of Weyl type may act upon a given irreducible tensor-spinor bundle V over a Riemannian manifold. Together with the analogous but easier problem involving actions of tensors of Einstein type, this enumerates the possible curvature actions on V.

In this paper, we give characterizations of a twisted product manifold to be a warped product manifold by imposing certain conditions on the Weyl conformal curvature tensor and the Weyl projective tensor. We also find similar results for multiply twisted product manifolds.