We consider an involutive automorphism of the conformal algebra and the resulting symmetric space. We display a new action of the conformal group which gives rise to this space. The space has an intrinsic symplectic structure, a group-invariant metric and connection, and serves as the model space for a new conformal gauge theory. ∗Electronic-mail: [email protected]

In this paper, we study the geometry of lightlike hypersurfaces of an indefinite trans-Sasakian manifold with a quarter-symmetric metric connection. The main result is a characterization theorem for such a lightlike hypersurface of an indefinite generalized Sasakian space form. Mathematics Subject Classification: 53C25, 53C40, 53C50

In Symmetric Teleparallel General Relativity, gravity is attributed to the non-metricity. The so-called "coincident gauge" usually taken in this theory so that affine connection vanishes and metric only fundamental variable. This gauge choice was kept many studies on extensions of such as f(Q) theory. paper, we point out sometimes will make inconsistent. To circumvent problem, reformulate a cov...

Abstract We discuss equivalent representations of gravity in the framework metric-affine geometries pointing out basic concepts from where these theories stem out. In particular, we take into account tetrads and spin connection to describe so called Geometric Trinity Gravity . Specifically, consider General Relativity, constructed upon metric tensor based on curvature R ; Teleparallel Equivalen...