Weidong SONG, Fen ZHOU

7187

Spherically symmetric Finsler metrics with Scalar Flag Curvature

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.

Anahtar Kelimeler:

Spherically symmetric, locally projectively flat, scalar flag curvature, error function

Spherically symmetric Finsler metrics with Scalar Flag Curvature

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.

Keywords:

Spherically symmetric, locally projectively flat, scalar flag curvature, error function,

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P = F

Turkish Journal of Mathematics-Cover

ISSN: 1300-0098
Yayın Aralığı: 6
Yayıncı: TÜBİTAK

Arşiv

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