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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+1F=0 and FW−(−)W+1F≠0 for 1<W<K, in the tangent bundle

international journal of mathematics and mathematical sciences

Complete lift of a structure satisfying<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$F^K - \left( - \right)^{K + 1} F = 0$"><mml:mrow><mml:msup><mml:mi>F</mml:mi><mml:mi>K</mml:mi></mml:msup><mml:mo>−</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mo>−</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>K</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mi>F</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math>

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