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



Das, Lovejoy;Nivas, Ram;Singh, Abhishek

  • 투고 : 2010.05.14
  • 심사 : 2010.09.27
  • 발행 : 2010.12.31


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




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