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On a Structure De ned by a Tensor Field F of Type (1, 1) Satisfying [F2+a(j)F+λ2(j)I]=0
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  • Journal title : Kyungpook mathematical journal
  • Volume 50, Issue 4,  2010, pp.455-463
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2010.50.4.455
 Title & Authors
On a Structure De ned by a Tensor Field F of Type (1, 1) Satisfying [F2+a(j)F+λ2(j)I]=0
Das, Lovejoy; Nivas, Ram; Singh, Abhishek;
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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 -structure satisfying However, 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,,, and obtain integrability conditions of the distributions and .
 Cited by
Lovejoy S. Das and Ram Nivas, On differentiable manifolds with [$F_1,\;F_2$](K + 1, 1) - structue, Tensor, N. S., 65(1) (2004), 29-35.

Lovejoy Das, Fiberings on almost r - contact manifolds, Publicationes Mathematicae, Debrecen, Hongrie, 43(1-2)(1993), 1-7.

Lovejoy Das, On CR - structures and F - structure satisfying $F^{K}+(-)^{K+1}F=0$, Rocky Mountain Journal of Mathematics, USA, 36(2006), 885-892. crossref(new window)

Lovejoy Das and Ram Nivas, Harmonic morphism on almost r - contact metric manifolds, Algebras Group and Geometries 22(2005), 61-68.

S. Helgason, Differential geometry, Lie groups and symmetric spaces, Academic Press, New York (1978).

S. Ishihara and K. Yano, On integrability conditions of a structure f satisfying $f^{3}+f=0$, Quart. J. Math., Oxford Sem (2) IS (1964), 217-222. crossref(new window)

R. S. Mishra, Structures on a Differentiable Manifold and their Applications, Chandrama Prakashan, 50-A, Balrampur House, Allahabad, India, 1984.

B. B. Sinha and R. Sharma, On a special quadratic structures on differentiable manifolds, Indian J. Pure Appl. Math., 9(8)(1978), 811-817.

K. Yano, On a structure defined by a tensor field f of type (1, 1) satisfying $f^{3}+f=0$, Tensor N. S., 14(1963), 99-109.