Geometric invariants under a SMRC-transformation group on manifolds and an application to asset pricing

Abstract

We investigate and confirm the geometric invariants under a SMRC-transformation group on manifolds and propose  an interesting asset pricing model via the geometric invariant and martingale idea in a financial market. In this case we achieve, for the first time, an interesting example for the category of invariant geometries with respect to  semi-symmetric connections.  By virtue of the projective conformal semi-symmetric metric recurrent connection  and the corresponding curvature tensors, the  celebrated  Schur's theorem, which is used to characterize the geometric properties of spaces, is  also obtained.