ON SOME CLASSES OF R-COMPLEX HERMITIAN FINSLER SPACES
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In this paper, we investigate the R-complex Hermitian Finsler spaces, emphasizing the differences that separate them from the complex Finsler spaces. The tools used in this study are the Chern-Finsler and Berwald connections. By means of these connections, some classes of the R-complex Hermitian Finsler spaces are defined, (e.g. weakly K¨ahler, K¨ahler, strongly K¨ahler). Here the notions of K¨ahler and strongly K¨ahler do not coincide, unlike the complex Finsler case. Also, some kinds of Berwald notions for such spaces are introduced. A special approach is devoted to obtain the equivalence conditions for an R-complex Hermitian Finsler space to become a weakly Berwald or Berwald. Finally, we obtain the conditions under which an R-complex Hermitian Finsler space with Randers metric is Berwald. We get some clear examples which illustrate the interest for this work.
Abstract
In this paper, we investigate the R-complex Hermitian Finsler spaces, emphasizing the differences that separate them from the complex Finsler spaces. The tools used in this study are the Chern-Finsler and Berwald connections. By means of these connections, some classes of the R-complex Hermitian Finsler spaces are defined, (e.g. weakly K¨ahler, K¨ahler, strongly K¨ahler). Here the notions of K¨ahler and strongly K¨ahler do not coincide, unlike the complex Finsler case. Also, some kinds of Berwald notions for such spaces are introduced. A special approach is devoted to obtain the equivalence conditions for an R-complex Hermitian Finsler space to become a weakly Berwald or Berwald. Finally, we obtain the conditions under which an R-complex Hermitian Finsler space with Randers metric is Berwald. We get some clear examples which illustrate the interest for this work.
참고문헌 (13)
- M. Abate, "Finsler Metrics - A Global Approach", Lecture Notes in Math., 1591 (1994), Springer-Verlag
- T. Aikou, "Finsler geometry on complex vector bundles, A sampler of Riemann-Finsler geometry", Math. Sci. Res. Inst. Publ., 50, pp.83~105 (2004), Cambridge Univ. Press
- Nicoleta Aldea, "On complex Finsler spaces with Randers metric", 대한수학회지, 46(5), pp.949~966 (2009), 대한수학회
- N. Aldea, "On complex Landsberg and Berwald spaces", J. Geom. Phys, 62(2), pp.368~380 (2012)
- N. Aldea, "On complex Douglas spaces", J. Geom. Phys, 66, pp.80~93 (2013)
- N. Aldea, "New candidates for a Hermitian approach of Gravity", Int. J. Geom. Methods Mod. Phys, 10(9), pp.22~ (2013)
- N. Aldea, "R-complex Finsler spaces with (α, β)-metric", Novi Sad J. Math, 38(1), pp.1~9 (2008)
- D. Bao, "An Introduction to Riemann-Finsler Geometry", Graduate Texts in Mathematics, 200, pp.200~ (2000), Springer-Verlag
- A. Bejancu, "Geometry of pseudo-Finsler submanifolds" (2000), Kluwer Academic Publishers
- L. Berwald, "Uber Finslersche und Cartansche Geometrie. IV", Ann. of Math, 48, pp.755~781 (1947)
- B. Chen, "K¨ahler Finsler metrics are actually strongly K¨ahler", Chin. Ann. Math. Ser. B, 30(2), pp.173~178 (2009)
- B. Chen, "On complex Randers metrics", Internat. J. Math, 21(8), pp.971~986 (2010)
- S. Kobayashi, "Complex Finsler vector bundles, Finsler geometry", Contemp. Math., 196, pp.145~153 (1996), Amer. Math. Soc.