On a Structure De ned by a Tensor Field F of Type (1, 1) Satisfying $\small{ \prod\limits_{j=1}^{k}}$[F2+a(j)F+λ2(j)I]=0

• 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 $\small{ \prod\limits_{j=1}^{k}}$[F2+a(j)F+λ2(j)I]=0
Das, Lovejoy; Nivas, Ram; Singh, Abhishek;

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 $\small{F_{a(j){\times}(j)}$-structure satisfying $\small{\prod\limits_{j=1}^{k}\;[F^2+a(j)F+\lambda^2(j)I]\;=\;0}$ 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,$\small{\ldots}$,$\small{K\;\in\;N}$, and obtain integrability conditions of the distributions $\small{\pi_m^j}$ and $\small{{\pi\limits^{\sim}}_m^j}$.
Keywords
$\small{F_{a(j),\lambda(j)}}$-structure;distribution;integrability;
Language
English
Cited by
References
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