Wyniki wyszukiwania - BazTech

1

On weakly symmetric generalized trans-sasakian manifold

Das L. S., Nivas R., Agnihotri R.

Commentationes Mathematicae

|

2014

|

Vol 54, No. 1

141--145

EN

In this paper, we have defined the weakly symmetric generalized Trans-Sasakian manifold G(WS)n and it has been shown that on such manifold if any two of the vector fields λ,γ,τ, defined by equation (0.3) are orthogonal to ξ, then the third will also be orthogonal to ξ. We have also proved that the scalar curvature r of weakly symmetric generalized Trans-Sasakian manifold G(WS)n, (n>2) satisfies the equation r=2n(α2−β2), where α and β are smooth function and γ≠τ.

2

Submanifolds immersed in a generalized Hsu quaternion manifold

Das L., Nivas R., Mishra M.

Demonstratio Mathematica

|

2006

|

Vol. 39, nr 3

639-642

EN

Integrability conditions of an almost quarternion manifold were studied by Yano and Ako [7]. Hamoui [1] and others have studied quaternion submanifolds of codimension 2 [1]. Vanzura [5] defined and have studied almost r- contact structure on manifolds. In this paper we have defined the Hsu-quaternion manifold and studied the submanifolds of codimension p immersed in a generalized Hsu quaternion manifold. Certain other interesting results have also been established.

3

On a special structure in a differentiable manifold

Nivas R., Saxena M.

Demonstratio Mathematica

|

2006

|

Vol. 39, nr 1

203-210

EN

K. Yano, studied structure defined by a tensor field f of type (1,1) satisfying f3 + f = 0. In this paper we have considered a structure of fourth order, which involves the generalization of the above structure. Some interesting results have been obtained on the existence and the integrability conditions of such a structure.

4

On horizontal and complete lifts of (1,1) tensor fields F satisfying the structure equation anFn+an-1Fn-1+an-2Fn-2+.......a2F2+a1F=0

Nivas R., Ali S., Srivastava S. K.

Demonstratio Mathematica

|

2002

|

Vol. 35, nr 1

155-163

EN

The horizontal and complete lifts from a differentiable manifold Mn of class C°° to its cotangent bundle T*(Mn) have been studied by Professors Yano and Patterson [5, 6]. Yano and Ishihara [7] studied lifts of f-structure in the tangent and cotangent bundles. F-structure manifolds of degree v > 3 have been studied by Kim [2]. Lifts of (1,1) tensor fields F satisfying Fv+2 - A2Fv-1 = 0 and Fv + (-l)v+1F = 0 have been studied by Srivastava [4]. The present paper deals with some problems on horizontal and complete lifts tensor fields satisfying polynomial equations of the type mentioned above. Integrability conditions are discussed, and prolongations in the third tangent space T3(Mn) are also considered.