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Weighted Quasi-Metrics Associated with Finsler Metrics
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The current paper deals with some new classes of Finsler metrics with reversible geodesics. We construct weighted quasi-metrics associated with these metrics. Further, we investigate some important geometric properties of weighted quasi-metric space. Finally, we discuss the embedding of quasi-metric spaces with generalized weight.
Keywords
Reversible Geodesics, Weighted Quasi-Metrics, Absolute Homogeneous Metrics, Metric Structure, Perimeter, Embedding.
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- D. Bao, S. S. Chern and Z. Shen, An Introduction to Riemann-Finsler Geometry, GTM, Vol. 200, Springer-Verlag, 2000.
- S. S. Chern and Z. Shen, Riemann-Finsler Geometry, Nankai Tracts Math., 6, World Sci. Publ., Singapore, 2005.
- M. Crampin, Randers spaces with reversible geodesics, Publ. Math. Debrecen, 67 (3-4) (2005), 401–409.
- G. Hamel, U¨ber die Geometrieen, in denen die Geraden die Ku¨rzesten sind, Math. Ann., 57 (1903), 231–264.
- H. P. A. K¨unzi and V. Vajner, Weighted quasi–metrics in: Papers on General topology and Appl., Annals New York Acad. Sci., 728 (1994), 64–77.
- I. M. Masca, S. V. Sabau and H. Shimada, Reversible geodesics for (α, β)-metrics, Int. J. Math., 21(8) (2010), 1071–1094.
- I. M. Masca, S. V. Sabau and H. Shimada, Necessary and sufficient conditions for two-dimensional (α, β)-metrics with reversible geodesics, preprint, arXiv:1203.1377V1[math.DG].
- S. G. Matthews, Partial metric topology in: Papers on General topology and Applications, Ninth summer Conf. Slippery. Rock, PA, Annals New York Acad. Sci., 767 (1993), 188–193.
- S. V. Sabau, K. Shibuya and H. Shimada, Metric structures associated to Finsler metrics, Publ. Math. Debrecen, 84(1-2) (2014), 89–103.
- S. V. Sabau and H. Shimada, Finsler manifolds with reversible geodesics, Rev. Roumaine Math. Pures Appl., 57(1) (2012), 91–103.
- G. Shanker and S. A. Baby, Reversible geodesics of Finsler spaces with a special (α, β)-metric, Bull. Cal. Math. Soc., 109(3) (2017), 183–188.
- Z. Shen and G. C. Yildrin, On a class of projectively flat metrics with constant flag curvature, Canad. Math. Bull., 60(2) (2008), 443–456.
- Z. Shen, On projectively flat (α, β)-metrics, Canad. Math. Bull., 52(1) (2009), 132–144.
- P. Vitolo, A representation theorem for quasi-metric spaces, Topology Appl., 65 (1995), 101–104.
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