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

• Autorzy: Nivas R. , Ali S. , Srivastava S. K.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

differentiable manifold; horizontal lifts

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2002
• Tom: Vol. 35, nr 1
• Strony: 155--163
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Nivas R.

• Department of Mathematics & Astronomy, University of Lucknow, Lucknow-226 007, India

autor

Ali S.

• Department of Mathematics & Astronomy, University of Lucknow, Lucknow-226 007, India

autor

Srivastava S. K.

• Department of Mathematics & Astronomy, University of Lucknow, Lucknow-226 007, India

Bibliografia

• [1] Ishihara, S., and Yano, K., On integrability of a structure f satisfying f3 + f = 0. Quart. Jour.Math. Oxford, 21 (1964), 217-222.
• [2] Kim, J. B.: Notes on f-manifolds. Tensor, N.S., 29 (1975), 299-302.
• [3] Nivas, R a m and Srivastava, S. K., On horizontal and complete lifts from a manifold with fλ (7, -1)-structure to its cotangent bundle. Jour. Tensor Soc. India, 14 (1996), 42-48.
• [4] Srivastava, S. K., On horizontal and complete lifts of (1,1) tensor field F satisfying structure […]. Ph.D Thesis, Lucknow University, India (1999).
• [5] Yano, K., and Patterson, E. M., Vertical and complete lifts from a manifold to its cotangent bundle. Jour. Math. Soc. Japan, 16 (1967), 91-113.
• [6] Yano, K., and Patterson, E. M., Horizontal lifts from a manifold to its cotangent bundle. Jour. Math. Soc. Japan, 19 (1967), 185-198.
• [7] Yano, K. and Ishihara, S., Tangent and cotangent bundles. Marcel Dekker Inc., New York (1973).