On Lie Differentiability Conditions of Some Polynomial Structures in Semi Tangent Bundle

Source abstract

In popular differential geometry, the tensor structures on smooth manifolds are remarkable geometric objects. In reality, every tensor structure is a polynomial structure. A tensor field f of type ( 1 , 1 ) on a differentiable manifold is called a polynomial structure if it satisfies the algebraic equation ( 1) 11.... f n + a 1 f ( n+ 1) + …. + a n -1 f + a n I = 0, where I is the identity tensor of type ( 1 , 1 ) and a 1 , a 2 ,..., a n are real numbers. The Lie differentiability conditions of some polynomial structures (almost contact and almost paracontact structures) in semi-tangent bundle t(M) are examined in this study.