Some Calculations on Kaluza-Klein Metric with Respect to Lifts in Tangent Bundle

Çayir H.

Boletim da Sociedade Paranaense de Matematica, vol.41, 2023 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 41
  • Publication Date: 2023
  • Doi Number: 10.5269/bspm.52990
  • Journal Name: Boletim da Sociedade Paranaense de Matematica
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH, Directory of Open Access Journals
  • Keywords: Kaluza-Klein metric, horizontal lift, vertical lift, tangent bundle, GEOMETRY
  • Karadeniz Technical University Affiliated: No

Abstract

© 2023 Boletim da Sociedade Paranaense de Matematica. All rights reserved.In the present paper, a Riemannian metric on the tangent bundle, which is another generalization of Cheeger-Gromoll metric and Sasaki metric, is considered. This metric is known as Kaluza-Klein metric in literature which is completely determined by its action on vector fields of type XH and Y V . We obtain the covarient and Lie derivatives applied to the Kaluza-Klein metric with respect to the horizontal and vertical lifts of vector fields, respectively on tangent bundle TM.