ON SOME CLASSES OF ℝ-COMPLEX HERMITIAN FINSLER SPACES

Title & Authors
ON SOME CLASSES OF ℝ-COMPLEX HERMITIAN FINSLER SPACES
Aldea, Nicoleta; Campean, Gabriela;

Abstract
In this paper, we investigate the $\small{\mathbb{R}}$-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 $\small{\mathbb{R}}$-complex Hermitian Finsler spaces are defined, (e.g. weakly K$\small{\ddot{a}}$hler, K$\small{\ddot{a}}$hler, strongly K$\small{\ddot{a}}$hler). Here the notions of K$\small{\ddot{a}}$hler and strongly K$\small{\ddot{a}}$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 $\small{\mathbb{R}}$-complex Hermitian Finsler space to become a weakly Berwald or Berwald. Finally, we obtain the conditions under which an $\small{\mathbb{R}}$-complex Hermitian Finsler space with Randers metric is Berwald. We get some clear examples which illustrate the interest for this work.
Keywords
$\small{\mathbb{R}}$-complex Hermitian Finsler space;Berwald space;Randers space;
Language
English
Cited by
1.
Geodesic Curves on $${\mathbb{R}}$$ R -Complex Finsler Spaces, Results in Mathematics, 2016, 70, 1-2, 15
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