Polynomial of second degree structures on big tangent bundle

Abstract

We introduced the generalized (a, b)-structure on a Riemannian manifold M, a notion that includes the generalized almost complex and generalized almost product structures. We studied the canonical generalized (a, b)-structure Jg induced by the Riemannian metric on M, afterward the generalized (a, b)-structure J_g induced by a similar structure on M. Considering a torsion-free linear connection ∇ on M, we define the ∇-integrability of a generalized (a, b)-structure, and conditions for ∇-integrability of J_g and  Ĵ are given.