A Class of Finsler Metrics with Almost Vanishing H- and \(\Xi \)-curvatures

Abstract

In this paper, we study \(\Xi \)-curvature and H-curvature of a special class of Finsler metrics called general \((\alpha ,\beta )\)-metrics. We prove that every general \((\alpha ,\beta )\)-metric of almost vanishing H-curvature is of almost vanishing \( \Xi \)-curvature under certain conditions. Moreover, we study such Finsler metric with vanishing \(\Xi \)-curvature and its interaction to the flag curvature.

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Acknowledgements

The paper was completed during the visit of the M.G. and B.R. to Istanbul Bilgi University. We are grateful to Istanbul Bilgi University for partial financial support and their hospitality. The authors sincerely thank the referees for their valuable suggestions and comments.

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Correspondence to Bahman Rezaei.

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Gabrani, M., Rezaei, B. & Sevim, E.S. A Class of Finsler Metrics with Almost Vanishing H- and \(\Xi \)-curvatures. Results Math 76, 44 (2021). https://doi.org/10.1007/s00025-021-01355-z

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Keywords

  • Finsler metric
  • general \((\alpha</Keyword> <Keyword>\beta )\)-metric
  • the H-curvature
  • almost vanishing \(\Xi \)-curvature

Mathematics Subject Classification

  • 53B40
  • 53C60