The Principal Fibre Bundle on Lorentzian Almost R-para Contact Structure

The purpose of this paper is to study the principal fibre bundle ( P , M , G , π p ) with Lie group G , where M admits Lorentzian almost paracontact structure ( Ø , ξ p , η p , g ) satisfying certain condtions on (1, 1) tensor field J , indeed possesses an almost product structure on the principal fibre bundle. In the later sections, we have defined trilinear frame bundle and have proved that the trilinear frame bundle is the principal bundle and have proved in Theorem 5.1 that the Jacobian map π * is the isomorphism.

An Overview of the History of Projective Representations of Groups

In this work we investigate the possible classes of seven-dimensional almost paracontact metric structures induced by the three-forms of $G_2^*$ structures. We write the projections that determine to which class the almost paracontact structure belongs, by using the properties of the $G_2^*$ structures. Then we study the properties that the characteristic vector field of the almost paracontact metric structure should have such that the structure belongs to a specific subclass of almost paracontact metric structures.

Generalized almost paracontact structures

The notion of generalized almost paracontact structure on the generalized tangent bundle TM ⊕ T* M is introduced and its properties are investigated. The case when the manifold M carries an almost paracontact metric structure is also discussed. Conditions for its transformed under a β- or a B-field transformation to be also a generalized almost paracontact structure are given. Finally, the normality of a generalized almost paracontact structure is defined and a characterization of a normal generalized almost paracontact structure induced by an almost paracontact one is given.

WEYL STRUCTURES ON ALMOST PARACONTACT MANIFOLDS

We introduce a new covariant differential A∇ adapted to an almost paracontact structure. We prove its relation with a Weyl structure and give some necessary and sufficient conditions for its harmonicity. We also characterize the P-Sasakian condition in terms of A∇.