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

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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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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran

    Mehran Gabrani & Bahman Rezaei

  2. Department of Mathematics, Istanbul Bilgi University, Eski Silahtaraga Elektrik Santrali, Kazim Karabekir Cad. No: 2/13 Eyupsultan, 34060, Istanbul, Turkey

    Esra Sengelen Sevim

Authors
  1. Mehran Gabrani
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  2. Bahman Rezaei
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  3. Esra Sengelen Sevim
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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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