Geometries for a mutual connection of semi-symmetric metric recurrent connections

Abstract

A semi-symmetric metric recurrent connection has already been studied. In this paper we newly discovered geometrical properties and conjugate symmetric condition for the mutual connection of a semi-symmetric metric recurrent connection in a Riemannian manifold.

Geometric characteristics of a manifold with a symmetric-type quarter-symmetric projective conformal non-metric connection

“…Following this concept and the related researches, Zhao, Ho, An [29], Zhao, Jen and Ho [30] further studied the geometrical properties of a manifold with Ricci quarter-symmetric recurrent connections and mutual connections. For this topics, one can also see [2,8,15,23,24,28] for details.…”

Geometric inequalities for non-integrable distributions in statistical manifolds with constant curvature

“…There are many applications in information geometry, which represents one of the main tools for machine learning and evolutionary biology. Since such a manifold is endowed with a pairing of torsion-free connections, called dual connections (or conjugate connections in affine geometry [12,14,18]), its geometry is closely related to affine differential geometry. Moreover, a statistical structure is a generalization of a Hessian structure.…”