On a Compendious Structure on a Differentiable Manifold

Abstract

In recent years several structures, notable almost contact atructure [2], [6], [8], almost r-contact structure [4],[15], almost paracontact structure [9], almost r-paracontact structure [2], almost contact hyperbolicstructure [14] and almost r-contact hyperbolic structure [5] have been defined and studied on a differentiable manifold by many geometers. Some generalized structures, including almost ) ,( 2 1 ee contact structure [10], almost ) ,( 2 1 ee -r-contact structure [11], [12] and unified structure [1], [13] have also been defined. In this paper, We define and study a compendious structure having the following structures as its special cases.