In this paper, we study submanifolds in a Riemannian manifold with a semi-symmetric non-metric connection. We prove that the induced connection on a submanifold is also semi-symmetric non-metric connection. We consider the total geodesicness and minimality of a submanifold with respect to the semi-symmetric non-metric connection. We obtain the Gauss, Cadazzi, and Ricci equations for submanifolds with respect to the semi-symmetric non-metric connection.

https://www.mdpi.com/2073-8994/9/7/112/pdf

On Submanifolds in a Riemannian Manifold with a Semi-Symmetric Non-Metric Connection

Projective invariants for equitorsion geodesic mappings of semi-symmetric affine connection spaces

We introduce a generalized quarter-symmetric metric recurrent connection and study its geometrical properties. We also derive the Schur’s theorem for the generalized quarter-symmetric metric recurrent connection.

/pdf/on-a-generalized-quarter-symmetric-metric-recurrent-3rx3la7p5h.pdf

On a generalized quarter symmetric metric recurrent connection

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.

/pdf/geometries-for-a-mutual-connection-of-semi-symmetric-metric-2ec9k85zvy.pdf

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

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.

/pdf/on-a-ricci-quarter-symmetric-metric-recurrent-connection-and-2la73t6hw9.pdf

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

The object of the present paper is to study a Riemannian manifold admitting a type of semi-symmetric non-metric connection whose torsion tensor is pseudo symmetric.

/pdf/a-special-type-of-semi-symmetric-non-metric-connection-on-a-2tgnz3qqas.pdf

Pei Biao Zhao

Papers

A special type of semi-symmetric non-metric connection on a riemannian manifold