Hostname: page-component-8448b6f56d-qsmjn Total loading time: 0 Render date: 2024-04-16T11:34:42.191Z Has data issue: false hasContentIssue false
  • English
  • Français

Projectively Flat Fourth Root Finsler Metrics

Published online by Cambridge University Press:  20 November 2018

Benling Li  and
Zhongmin Shen
Benling Li
Affiliation:
Department of Mathematics, Ningbo University, Ningbo, Zhejiang Province 315211, P.R. China e-mail: libenling@nbu.edu.cn
Zhongmin Shen
Affiliation:
Center of Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang Province 310027, P.R. China, and Department of Mathematical Sciences, Indiana University Purdue University Indianapolis (IUPUI), 402 N. Blackford Street, Indianapolis, IN 46202-3216, USA e-mail: zshen@math.iupui.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, we study locally projectively flat fourth root Finsler metrics and their generalized metrics. We prove that if they are irreducible, then they must be locally Minkowskian.

Keywords

53B40projectively flatFinsler metricfourth root Finsler metric
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 55 , Issue 1 , 01 March 2012 , pp. 138 - 145
Copyright
Copyright © Canadian Mathematical Society 2012

References

[1] Brinzei, N., Projective relations for m-th root metric spaces. J. Calcutta Math. Soc. 5(2009), no. 1-2, 21–35.Google Scholar
[2] Berwald, L., Parallelúbertragung in allgemeinen Räumen. Atti Congr. Intern. Mat. Bologna 4(1928), 263–270.Google Scholar
[3] Berwald, L., Über die n-dimensionalen Geometrien konstanter Krümmung, in denen die Geraden die kürzesten sind. Math. Z. 30(1929), 449–469. doi:10.1007/BF01187782Google Scholar
[4] Berwald, L., On Finsler and Cartan geometries. III. Two-dimensional Finsler spaces with vectilinear extremals. Ann. of Math. 42(1941), 84–112. doi:10.2307/1968989Google Scholar
[5] Kim, B. and Park, H., The m-th root Finsler metrics admitting (α, β)-types. Bull. Korean Math. Soc. 41(2004), no. 1, 45–52. doi:10.4134/BKMS.2004.41.1.045Google Scholar
[6] Li, B. and Shen, Z., On a class of projectively flat Finsler metrics with constant flag curvature. Internat. J. Math. 18(2007), no. 7, 749–760. doi:10.1142/S0129167X07004291Google Scholar
[7] Matsumoto, M., Theory of Finsler spaces with m-th root metric. II. Publ. Math. Debrecen 49(1996) no. 1-2, 135–155.Google Scholar
[8] Matsumoto, M. and Okubo, K., Theory of Finsler spaces with mth root metric: Connecions and main scalars. Tensor (N.S.) 56(1995), no. 1, 93–104.Google Scholar
[9] Numata, S., On Landsberg spaces of scalar curvature. J. Korea Math. Soc. 12(1975), no. 2, 97–100.Google Scholar
[10] Pavlov, D. G. (ed.), Space-Time Structure. Collected papers. TETRU, Moscow, 2006.Google Scholar
[11] Shen, Z., Projectively flat Finsler metrics of constant flag curvature. Trans. Amer. Math. Soc. 355(2003), no. 4, 1713–1728. doi:10.1090/S0002-9947-02-03216-6Google Scholar
[12] Shen, Z., On projectively flat (α, β)-metrics. Canad. Math. Bull. 52(2009), no. 1, 132–144. doi:10.4153/CMB-2009-016-2Google Scholar
[13] Shimada, H., On Finsler spaces with the metric L = , Tensor (N.S.) 33(1979), 365–372.Google Scholar