On projective invariants of the complex Finsler spaces
Differential Geometry
2011-06-07 v1
Abstract
In this paper the projective curvature invariants of a complex Finsler space are obtained. By means of these invariants the notion of complex Douglas space is then defined. A special approach is devoted to obtain the equivalence conditions that a complex Finsler space should be Douglas. It is shown that any weakly K\"{a}hler Douglas space is a complex Berwald space. A projective curvature invariant of Weyl type characterizes the complex Berwald spaces. They must be either purely Hermitian of constant holomorphic curvature or non purely Hermitian of vanish holomorphic curvature. The locally projectively flat complex Finsler metrics are also studied
Keywords
Cite
@article{arxiv.1106.0894,
title = {On projective invariants of the complex Finsler spaces},
author = {Nicoleta Aldea and Gheorghe Munteanu},
journal= {arXiv preprint arXiv:1106.0894},
year = {2011}
}