Geodesic
Finsler structures on holomorphic Lie algebroids
Novi Sad Journal of Mathematics, Tome 47 (2017) no. 2.

Voir la notice de l'article provenant de la source Novi sad journal of mathematics website

Complex Finsler vector bundles have been studied mainly by T. Aikou, who defined complex Finsler structures on holomorphic vector bundles. In this paper, we consider the more general case of a holomorphic Lie algebroid $E$ and we introduce Finsler structures, partial and Chern-Finsler connections on it. First, we recall some basic notions on holomorphic Lie algebroids. Then, using an idea from E. Martinez, we introduce the concept of complexified prolongation of such an algebroid. Also, we study nonlinear and linear connections on the tangent bundle $T_{\mathbb{C}}E$ and on the prolongation $\mathcal{T}_{\mathbb{C}}E$ and we investigate the relation between their coefficients. The analogue of the classical Chern-Finsler connection is defined and studied in the paper for the case of the holomorphic Lie algebroid $E$.
Publié le :
DOI : 10.30755/NSJOM.05838
Classification : 17B66, 53B35, 53B40
Keywords: Holomorphic Lie algebroid, anchor map, Finsler nonlinear connection, prolongation, Lagrangian structures 
@article{10.30755/NSJOM.05838,
     author = {Alexandru Ionescu},
     title = {Finsler structures on holomorphic {Lie} algebroids},
     journal = {Novi Sad Journal of Mathematics},
     pages = {117 - 132},
     publisher = {mathdoc},
     volume = {47},
     number = {2},
     year = {2017},
     doi = {10.30755/NSJOM.05838},
     url = {http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.05838/}
}
TY  - JOUR
AU  - Alexandru Ionescu
TI  - Finsler structures on holomorphic Lie algebroids
JO  - Novi Sad Journal of Mathematics
PY  - 2017
SP  - 117 
EP  -  132
VL  - 47
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.05838/
DO  - 10.30755/NSJOM.05838
ID  - 10.30755/NSJOM.05838
ER  - 
%0 Journal Article
%A Alexandru Ionescu
%T Finsler structures on holomorphic Lie algebroids
%J Novi Sad Journal of Mathematics
%D 2017
%P 117 - 132
%V 47
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.05838/
%R 10.30755/NSJOM.05838
%F 10.30755/NSJOM.05838
Alexandru Ionescu. Finsler structures on holomorphic Lie algebroids. Novi Sad Journal of Mathematics, Tome 47 (2017) no. 2. doi : 10.30755/NSJOM.05838. http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.05838/

Cité par Sources :