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Classification of Three-Dimensional Left-Invariant Ricci-Quadratic Randers Metrics and its Applications | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 28 تیر 1404 اصل مقاله (1.19 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.66684.3141 | ||
| نویسندگان | ||
| Behzad Najafi* 1؛ Akbar Tayebi2؛ Fatemeh Barati2 | ||
| 1Department of Mathematics and Computer Sciences, Amirkabir University of Technology (Tehran Polytechnic), Tehran. Iran. | ||
| 2Department of Mathematics, Faculty of Science, University of Qom. Qom. Iran. | ||
| چکیده | ||
| In this paper, we establish necessary and sufficient conditions for a left-invariant Randers metric to be Ricci-quadratic. Using Ha-Bumlees classification of left-invariant Riemannian metrics and our characterization of left-invariant Ricci-quadratic Randers metrics, we classify all left-invariant Ricci-quadratic Randers metrics on three-dimensional Lie groups. As an application, we provide a counterexample to Hu-Dengs theorem [HD], which asserts that a homogeneous Randers metric is Ricci-quadratic if and only if it is Berwald. This demonstrates that Shen's rigidity theorem for R-quadratic metrics does not extend to Ricci-quadratic Finsler metrics. Furthermore, we show that our counterexample is a generalized Berwald metric (non-Berwaldian), as well as a generalized Douglas-Weyl metric that is neither Douglas, Weyl, nor projectively flat. | ||
| کلیدواژهها | ||
| Left-invariant metric؛ Randers metric؛ R-quadratic metric؛ Ricci-quadratic metric؛ Berwald metric | ||
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