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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

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

Demonstratio Mathematica

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.