G-structures of second order defined by linear operators satisfying algebraic relations

Abstract

The present work is based on a type of structures on a differential manifold V , called G-structures of the second kind, defined by endomorphism J on the second order tangent bundle T 2 (V). Our objective is to give conditions for a differential manifold to admit a real almost product and a generalised almost tangent structure of second order. The concepts of the second order frame bundle H 2 (V), its structural group L 2 and its associated tangent bundle of second order T 2 (V) of a differentiable manifold V , are used from the point of view that is described in papers [5] and [6]. Also, the almost tangent structure of order two is mentioned and its generalisation, the second order almost transverse structure, is defined.