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http://dx.doi.org/10.4134/JKMS.2015.52.3.587

ON SOME CLASSES OF ℝ-COMPLEX HERMITIAN FINSLER SPACES  

Aldea, Nicoleta (Department of Mathematics and Informatics Transilvania University)
Campean, Gabriela (Department of Mathematics and Informatics Transilvania University)
Publication Information
Journal of the Korean Mathematical Society / v.52, no.3, 2015 , pp. 587-601 More about this Journal
Abstract
In this paper, we investigate the $\mathbb{R}$-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 $\mathbb{R}$-complex Hermitian Finsler spaces are defined, (e.g. weakly K$\ddot{a}$hler, K$\ddot{a}$hler, strongly K$\ddot{a}$hler). Here the notions of K$\ddot{a}$hler and strongly K$\ddot{a}$hler 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 $\mathbb{R}$-complex Hermitian Finsler space to become a weakly Berwald or Berwald. Finally, we obtain the conditions under which an $\mathbb{R}$-complex Hermitian Finsler space with Randers metric is Berwald. We get some clear examples which illustrate the interest for this work.
Keywords
$\mathbb{R}$-complex Hermitian Finsler space; Berwald space; Randers space;
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