Complete lift of a structure satisfyingFK−(−)K+1F=0

Lovejoy S Das

doi:10.1155/s0161171292001042

Abstract

The idea off-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 manifoldMnof classC∞to its cotangent bundles have been studied by Yano and Patterson [4,5]. Yano and Ishihara [6] have studied lifts of anf-structure in the tangent and cotangent bundles. The purpose of this paper is to obtain integrability conditions of a structure satisfyingFK−(−)K+1F=0andFW−(−)W+1F≠0for1<W<K, in the tangent bundle.

Highlights

Let F be a nonzero tensor field of the type (i,i) and of class Coo on an n dimensional manifold Mn such that [7]FK (_)K+I F 0 and FW _(_)W+I F 0 for 1 < W < K,(I.i) where K is a fixed positive integer greater than 2
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]
Tsr(Mn), Let us denote by the set of all tensor fields of class C and of type n. (r,s) in Mn and T(Mn) be the tangent bundle over M The complete lift Fc of an TII(M element of n) with local components h

Summary

COMPLETE LIFT OF A STRUCTURE SATISFYING

Kent State University Tuscarawas Campus New Philadelphia, Ohio 44663 (Received August 30, 1991 and in revised form January 12, 1992) ABSTRACT. The idea of f-structure manifold on a differentiable manifold was initiated and developed by Yano [i], 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 s’tructure satisfying FK (-)K+IF 0 and Fw (-)W+IF 0 for 1 < W < K, in the tangent bundle.

INTRODUCTION

Fi ih h

COHYLETE LIFT OF A STRUCTURE IN THE TANGENT BUDDLE