Riemannian manifolds admitting a new type of semisymmetric nonmetric connection

Chaubey S. K., YILDIZ A.

TURKISH JOURNAL OF MATHEMATICS, vol.43, no.4, pp.1887-1904, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 43 Issue: 4
  • Publication Date: 2019
  • Doi Number: 10.3906/mat-1902-2
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1887-1904
  • Inonu University Affiliated: Yes

Abstract

We define a new type of semisymmetric nonmetric connection on a Riemannian manifold and establish its existence. It is proved that such connection on a Riemannian manifold is projectively invariant under certain conditions. We also find many basic results of the Riemannian manifolds and study the properties of group manifolds and submanifolds of the Riemannian manifolds with respect to the semisymmetric nonmetric connection. To validate our findings, we construct a nontrivial example of a 3-dimensional Riemannian manifold equipped with a semisymmetric nonmetric connection.