On a Ricci quarter-symmetric metric recurrent connection and a projective Ricci quarter-symmetric metric recurrent connection in a Riemannian manifold

Abstract

Two new types of connections, Ricci quarter-symmetric metric recurrent connection and projective Ricci quarter-symmetric metric recurrent connection, were introduced and some interesting geometrical and physical characteristics were achieved.

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

“…Remark 2.1. The quarter-symmetric non-metric connection family t ∇ is a connection homotopy of the quartersymmetric metric connection q ∇ in [30] and the quarter-symmetric non-metric connection n ∇.…”

“…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.…”