Classification of three-dimensional left-invariant Ricci-quadratic Randers metrics and their applications

Najafi, Behzad; Tayebi, Akbar; Barati, Fatemeh

doi:10.22034/cmde.2025.66684.3141

Classification of three-dimensional left-invariant Ricci-quadratic Randers metrics and their applications

Document Type : Research Paper

Authors

¹ Department of Mathematics and Computer Sciences, Amirkabir University of Technology (Tehran Polytechnic), Tehran. Iran.

² Department of Mathematics, Faculty of Science, University of Qom. Qom. Iran.

10.22034/cmde.2025.66684.3141

Abstract

In this paper, we determine the necessary and sufficient conditions for a left-invariant Randers metric to be a Ricci-quadratic metric. Then, by using HaBumlee’s classification of left-invariant Riemannian metrics and our characterization of Ricci-quadratic left-invariant Randers metrics, we give the classification of left-invariant Ricci-quadratic Randers metrics on three-dimensional Lie groups. As an application, we find an interesting Ricci-quadratic Randers metric on $SU(2)$ which is a generalized Berwald metric, while it is not Berwaldian. Also, we prove that it is a generalized Douglas-Weyl metric which is neither Douglasian nor a Weyl metric.

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References

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