IIARD International Institute of Academic Research and Development

RESEARCH JOURNAL OF PURE SCIENCE AND TECHNOLOGY (RJPST )

E-ISSN 2579-0536
P-ISSN 2695-2696
VOL. 8 NO. 5 2025
DOI: 10.56201/rjpst.vol.8.no5.2025.pg120.132

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Nickel Structure on a Differentiable Manifold

Ibrahim Isah, Mustapha Usman Baba, Nafisatu Muhammad Usman, Ahmad Nasidi, Umar, Aminu Muhammad Yusuf, Tijjani Lawal Hassan

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Abstract

We introduce a novel geometric structure on a differentiable manifold, which we call a nickel structure. This structure is defined by a tensor field ? of type (1,1) satisfying the algebraic equation ?2 ???3?= 0, where ? denotes the identity tensor. The defining equation leads to a natural decomposition of the tangent bundle into invariant subspaces characterized by two distinct eigenvalues, we determine the integrability of this decomposition through related almost product structure. We also, investigate the connection and parallelism of the nickel structure, and whether ? is preserved under a specific affine connection, including the Schouten and Vr? ?nceanu connection. Furthermore, we extend the concept of Riemannian geometry by defining a nickel Riemannian structure, where ? is compatible with the Riemannian metric ?.

keywords:

almost product structure, Nickel structure, integrability, Nickel Riemannian Manifold

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