Nickel Structure on a Differentiable Manifold
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 ?.
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