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On Lifts of Structure Satisfying F^(K+1)-a²F^(K-1)= 0
Lovejoy S. Das KYUNGPOOK UNIVERSITY 1998 Kyungpook mathematical journal Vol.38 No.1
The horizontal and complete lifts from a differentiable manifold Mⁿ of class C^(∞) to its cotangent bundles¤ T(Mⁿ) have been studied by Yano and Patterson [10, 11]. Yano and Ishihara [9] studied lifts of an f-structure in the tangent and cotangent bundles. The present paper deals with some problems on horizontal and complete lifts of F((K + 1),-a²(K-1))-structure (K, odd and≥ 3), both in tangent and cotangent bundles and the prolongations in the second tangent space T²(Mⁿ). The results of this paper have been announced by the author in Abstracts American Mathematical Society [2].
On a Differentiable Manifold with F-Structure of Rank r
Lovejoy S. Das KYUNGPOOK UNIVERSITY 2000 Kyungpook mathematical journal Vol.40 No.2
The results of f-structures manifold on a differentiable manifold was initiated and developed by Yano [1], Ishihara and Yano [2]. J. B. Kim [3] has defined and studied the structure of rank r and of degree k. The purpose of this paper is to study a differentiable manifold with F-structure of rank r using tensor as a vector valued linear function [4]. The case when k is odd and even have been considered in this paper.
Das, Lovejoy,Nivas, Ram,Singh, Abhishek Department of Mathematics 2010 Kyungpook mathematical journal Vol.50 No.4
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 ${\pi\limits^{\sim}}_m^j$.
Bailey pairs and strange identities
Jeremy Lovejoy 대한수학회 2022 대한수학회지 Vol.59 No.5
Zagier introduced the term ``strange identity" to describe an asymptotic relation between a certain $q$-hypergeometric series and a partial theta function at roots of unity. We show that behind Zagier's strange identity lies a statement about Bailey pairs. Using the iterative machinery of Bailey pairs then leads to many families of multisum strange identities, including Hikami's generalization of Zagier's identity.
Upadhyay, M.D.,Das, Lovejoy S.K. Department of Mathematics 1978 Kyungpook mathematical journal Vol.18 No.2
The first part of this paper is devoted to the study of F-structure satisfying: $F^K+(-)^{K+1}F=0$ and $F^W+(-)^{W+1}F{\neq}0$, for 1<W<K. The case when K is odd and K($${\geq_-}3$$) has been considered. In the later part some structures involving Lie-derivatives. exterior and co-derivatives have been studied.