Physics and geometries of a manifold associated with a generalized quarter-symmetric non-metric connection

Abstract

The present paper investigates  the fundamental physical invariants under some transform groups, and confirms some geometric characteristics of a manifold  associated with some connections. This article firstly introduces a generalized quarter-symmetric non-metric connection family and studies systematically its geometrical properties. The present paper also  arrives at  the interesting projective invariant of the generalized quarter-symmetric non-metric connection family.