Theoretical Mathematics & Applications

On a General Even Order Structure on a Differentiable Manifold

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• Abstract

  K. Yano defined and studied the structures defined by a tensorfield f ( 0) of type (1, 1) satisfying f³ + f = 0,  f⁴+f² = 0 ([1], [3]). In this paper, we have considered the structure of order 2n defined by (1, 1) tensorfield f where n is a positive integer. Certain interesting results have been obtained. Local coordinate system is introduced in the manifold and it has been shown that there exist complementary distributions L^* and M^* and a positive definite Riemannian metric G such that they are orthogonal.