Kropina Metrics with Isotropic Scalar Curvature via Navigation Data

被引：1

作者：

Ma, Yongling ^{[1
]}

Zhang, Xiaoling ^{[1
]}

Zhang, Mengyuan ^{[1
]}

机构：

[1] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830017, Peoples R China

来源：

MATHEMATICS | 2024年 / 12卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Kropina metrics; scalar curvature; Einstein metrics; ZERMELO NAVIGATION;

D O I：

10.3390/math12040505

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Through an interesting physical perspective and a certain contraction of the Ricci curvature tensor in Finsler geometry, Akbar-Zadeh introduced the concept of scalar curvature for the Finsler metric. In this paper, we show that the Kropina metric is of isotropic scalar curvature if and only if F is an Einstein metric according to the navigation data. Moreover, we obtain the three-dimensional rigidity theorem for an Einstein-Kropina metric.

引用

页数：10

共 50 条

[1] Kropina Metrics with Isotropic Scalar Curvature
Liu, Liulin
Zhang, Xiaoling
Zhao, Lili
[J]. AXIOMS, 2023, 12 (07)
[2] On Kropina metrics of scalar flag curvature
Xia, Qiaoling
[J]. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2013, 31 (03) : 393 - 404
[3] ON THE SCALAR CURVATURE OF KROPINA METRICS I
Zhu, Hongmei
Song, Lumin
[J]. HOUSTON JOURNAL OF MATHEMATICS, 2023, 49 (03): : 579 - 602
[4] On m-Kropina Finsler Metrics of Scalar Flag Curvature
Yang, Guojun
[J]. RESULTS IN MATHEMATICS, 2019, 74 (01)
[5] On m-Kropina Finsler Metrics of Scalar Flag Curvature
Guojun Yang
[J]. Results in Mathematics, 2019, 74
[6] On Randers metrics of isotropic scalar curvature
Cheng, Xinyue
Yuan, Mingao
[J]. PUBLICATIONES MATHEMATICAE-DEBRECEN, 2014, 84 (1-2): : 63 - 74
[7] ON THE CURVATURE OF INVARIANT KROPINA METRICS
Moghaddam, H. R. Salimi
[J]. INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY, 2011, 4 (02): : 136 - 140
[8] Kropina metrics and Zermelo navigation on Riemannian manifolds
Ryozo Yoshikawa
Sorin V. Sabau
[J]. Geometriae Dedicata, 2014, 171 : 119 - 148
[9] ON CONFORMALLY FLAT POLYNOMIAL (α, β)-METRICS WITH WEAKLY ISOTROPIC SCALAR CURVATURE
Chen, Bin
Xia, KaiWen
[J]. JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2019, 56 (02) : 329 - 352
[10] ON 4-TH ROOT METRICS OF ISOTROPIC SCALAR CURVATURE
Tayebi, Akbar
[J]. MATHEMATICA SLOVACA, 2020, 70 (01) : 161 - 172

← 1 2 3 4 5 →