On Einstein Finsler metrics

ÜLGEN S., ŞENGELEN SEVİM E., Hacınlıyan İ.

INTERNATIONAL JOURNAL OF MATHEMATICS, vol.32, no.09, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 32 Issue: 09
  • Publication Date: 2021
  • Doi Number: 10.1142/s0129167x21500634
  • Journal Name: INTERNATIONAL JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, DIALNET, Civil Engineering Abstracts
  • Keywords: (alpha, beta)-metrics, Einstein metrics, Ricci curvature, Ricci-flat
  • Istanbul Technical University Affiliated: Yes

Abstract

In this paper, we study Finsler metrics expressed in terms of a Riemannian metric, a 1-form, and its norm and find equations with sufficient conditions for such Finsler metrics to become Ricci-flat. Using certain transformations, we show that these equations have solutions and lead to the construction of a large and special class of Einstein metrics.