Lovejoy S. Das

On semi-invariant submanifolds of a nearly Sasakian manifold admitting a semi-symmetric non-metric connection

Abstract We define a semi-symmetric non-metric connection in a nearly Sasakian manifold and we consider semi-invariant submanifolds of a nearly Sasakian manifold endowed with a semi-symmetric non-metric connection. Moreover, we also obtain integrability conditions of the distributions on semi-invariant submanifolds.

On horizontal and complete lifts from a manifold with fλ(7,1)-structure to its cotangent bundle

The horizontal and complete lifts from a manifold M n to its cotangent bundles T ∗ ( M n ) were studied by Yano and Ishihara, Yano and Patterson, Nivas and Gupta, Dambrowski, and many others. The purpose of this paper is to use certain methods by which f λ ( 7 , 1 ) -structure in M n can be extended to T ∗ ( M n ) . In particular, we have studied horizontal and complete lifts of f λ ( 7 , 1 ) -structure from a manifold to its cotangent bundle.

On a structure satisfying FK−(−)K

In this paper we shall obtain certain results on the structure defined by F(K,−(−)K

Complete lift of a structure satisfying FK−(−)K

The idea of f-structure manifold on a differentiable manifold was initiated and developed by Yano [1], Ishihara and Yano [2], Goldberg [3] and among others. The horizontal and complete lifts from a differentiable manifold Mn of class C∞ to its cotangent bundles have been studied by Yano and Patterson [4,5]. Yano and Ishihara [6] have studied lifts of an f-structure in the tangent and cotangent bundles. The purpose of this paper is to obtain integrability conditions of a structure satisfying FK−(−)K

On Tachibana and Vishnevskii Operators Associated with Certain Structures in the Tangent Bundle

The aim of the present work is to study the complete, vertical and horizontal lifts using Tachibana and Visknnevskii operators along generalized almost r-contact structure in tangent bundle. We also prove certain theorems on Tachibana and Visknnevskii operators with Lie derivative and lifts.

On semi-invariant submanifolds of a nearly trans-Sasakian manifold admitting a semi-symmetric semi-metric connection

Abstract We define a semi-symmetric semi-metric connection in a nearly trans-Sasakian manifold and we consider semi-invariant submanifolds of a nearly trans-Sasakian manifold endowed with a semi-symmetric semi-metric connection. Moreover, we also obtain integrability conditions of the distributions on semi-invariant submanifolds.

On a Structure De ned by a Tensor Field F of Type (1, 1) Satisfying

The differentiable manifold with f - structure were studied by many authors, for example: K. Yano [7], Ishihara [8], Das [4] among others but thus far we do not know the geometry of manifolds which are endowed with special polynomial -structure satisfying However, special quadratic structure manifold have been defined and studied by Sinha and Sharma [8]. The purpose of this paper is to study the geometry of differentiable manifolds equipped with such structures and define special polynomial structures for all values of j = 1, 2,,, and obtain integrability conditions of the distributions and .

\prod\limits_{j=1}^{k}

The purpose of this paper is to study invariant submanifolds of an n- dimensional manifold M endowed with an F -structure satisfying F K + (−)K+1F = 0 and F W + (−) W +1 F ≠ 0 for 1 <W < K, where K is a fixed positive integer greater than 2. The case when K is odd (≥ 3) has been considered in this paper. We show that an in- variant submanifold ˜ M, embedded in an F -structure manifold M in such a way that the complementary distribution Dm is never tangential to the invariant submanifold Ψ ( ˜ M) ,i s an almost complex manifold with the induced ˜ F -structure. Some theorems regarding the integrability conditions of induced ˜ F -structure are proved.

[F 2 +a(j)F+λ 2 (j)I]=0

A study of prolongations of F-structure to the tangent bundle of order 2 has been presented.