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Some projectively Ricci-flat \((\alpha , \beta )\)-metrics

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Abstract

In this paper, we construct some projectively Ricci-flat Finsler metrics defined by a Riemannian metric \(\alpha \) and a 1-form \(\beta \). Moreover, we classify the projectively Ricci-flat \((\alpha , \beta )\)-metrics under the condition, that \(\beta \) is a non-parallel Killing form which has non-zero constant length.

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Authors and Affiliations

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

    Mehran Gabrani

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

    Esra Sengelen Sevim

  3. Department of Mathematical Sciences, Indiana University-Purdue University, Indianapolis, IN, 46202, USA

    Zhongmin Shen

Authors
  1. Mehran Gabrani
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  2. Esra Sengelen Sevim
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  3. Zhongmin Shen
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Correspondence to Zhongmin Shen.

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Gabrani, M., Sevim, E.S. & Shen, Z. Some projectively Ricci-flat \((\alpha , \beta )\)-metrics. Period Math Hung 86, 514–529 (2023). https://doi.org/10.1007/s10998-022-00486-2

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  • DOI: https://doi.org/10.1007/s10998-022-00486-2

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