On a Structure Defined by a Tensor Field F of Type (1, 1) Satisfying Πj=1k [F2 + a(j)F + λ2(j)I] = 0
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The differentiable manifold with f – structure were studied by many authors,for example: K. Yano [7], Ishihara [8], Das [4] among others but thus far we do not know the geometry of manifolds which are endowed with special polynomial Fa(j)x(j) – structure satisfying Πj=1k[F2 + a (j) F + λ2 (j) I]= 0However, special quadratic structure manifold have been defined and studied by Sinha and Sharma [8]. The purpose of this paper is to study the geometry of differentiable manifolds equipped with such structures and define special polynomial structures for all values of j = 1,2,...,K ∈ N, and obtain integrability conditions of the distributions πmj and πmj
Abstract
The differentiable manifold with f – structure were studied by many authors,for example: K. Yano [7], Ishihara [8], Das [4] among others but thus far we do not know the geometry of manifolds which are endowed with special polynomial Fa(j)x(j) – structure satisfying Πj=1k[F2 + a (j) F + λ2 (j) I]= 0However, special quadratic structure manifold have been defined and studied by Sinha and Sharma [8]. The purpose of this paper is to study the geometry of differentiable manifolds equipped with such structures and define special polynomial structures for all values of j = 1,2,...,K ∈ N, and obtain integrability conditions of the distributions πmj and πmj
참고문헌 (9)
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- B. B. Sinha, "On a special quadratic structures on differentiable manifolds", Indian J. Pure Appl. Math., 9(8), pp.811~817 (1978)
- K. Yano, "On a structure defined by a tensor field f of type (1, 1) satisfying f3+f = 0", Tensor N. S., 14, pp.99~109 (1963)