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2 Demonstratio Mathematica

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On a special structure in a differentiable manifold

100%

Nivas R. , Saxena M.

tom Vol. 39, nr 1

203-210

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.

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

80%

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

2002

tom Vol. 35, nr 1

155-163

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.