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Kropina Metrics with Isotropic Scalar Curvature via Navigation Data

Author

Listed:
  • Yongling Ma

    (College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China)

  • Xiaoling Zhang

    (College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China)

  • Mengyuan Zhang

    (College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China)

Abstract

Through an interesting physical perspective and a certain contraction of the Ricci curvature tensor in Finsler geometry, Akbar-Zadeh introduced the concept of scalar curvature for the Finsler metric. In this paper, we show that the Kropina metric is of isotropic scalar curvature if and only if F is an Einstein metric according to the navigation data. Moreover, we obtain the three-dimensional rigidity theorem for an Einstein–Kropina metric.

Suggested Citation

  • Yongling Ma & Xiaoling Zhang & Mengyuan Zhang, 2024. "Kropina Metrics with Isotropic Scalar Curvature via Navigation Data," Mathematics, MDPI, vol. 12(4), pages 1-10, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:4:p:505-:d:1334589
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