Affiliation:
1. College of Mathematics and Systems Sicence, Xinjiang University, Urumqi 830017, China
Abstract
In this paper, we study conformal transformations between two almost regular general (α,β)-metrics. By using the method of special coordinate system, the necessary and sufficient conditions for conformal transformations preserving the mean Landsberg curvature are obtained. Further, a rigidity theorem for regular general (α,β)-metrics is proved.
Funder
National Natural Science Foundation of China
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference12 articles.
1. Conformal geometry of generalised metric spaces;Knebelman;Proc. Natl. Acad. Sci. USA,1929
2. Finsler conformal transformations and the curvature invariances;Cheng;Publ. Math. Debr.,2007
3. On conformal transformations between two (α,β)-metrics;Chen;Differ. Geom. Appl.,2013
4. On conformal transformations between two almost regular (α,β)-metrics;Chen;Bull. Korean Math. Soc.,2018
5. On a class of weakly Landsberg metrics;Li;Sci. China Math.,2007