Geometries and topologies of a manifold with π-quarter-symmetric projective conformal and mutual connections

Abstract

We propose a new ?-quarter-symmetric projective conformal connection family and its mutual connection family and study its geometrical properties. We also arrive at the Schur?s theorem based on a symmetric-type ?-quarter-symmetric non-metric connection and investigate its geometrical property. This paper will pose a new grid computing method on manifolds, which will be done in our next topic.