Dergiler / Turkish Journal of Mathematics / 2015 / Cilt: 39 - Sayı: 1
Spherically symmetric Finsler metrics with Scalar Flag Curvature
- Sayfa
- 16–22
- DOI
- —
Özet
In this paper, we study spherically symmetric Finsler metrics F=|y|f(|x|,\frac{}{|y|}), where x \in Bn(r) \subset Rn, y \in TxBn(r)\{0} and f:[0,r)\times R \rightarrow R. By investigating a PDE equivalent to these metrics being locally projectively flat, we manufacture projectively flat spherically symmetric Finsler metrics in terms of error functions and, using Shen's result, we give its flag curvature.
Abstract
In this paper, we study spherically symmetric Finsler metrics F=|y|f(|x|,\frac{}{|y|}), where x \in Bn(r) \subset Rn, y \in TxBn(r)\{0} and f:[0,r)\times R \rightarrow R. By investigating a PDE equivalent to these metrics being locally projectively flat, we manufacture projectively flat spherically symmetric Finsler metrics in terms of error functions and, using Shen's result, we give its flag curvature.