Geodesic
On Riemannian and Ricci curvatures of homogeneous Finsler manifolds
Canadian mathematical bulletin, Tome 68 (2025) no. 1, pp. 73-90

Voir la notice de l'article provenant de la source Cambridge

DOI

The famous Cheng-Shen’s conjecture in Riemann-Finsler geometry claims that every n-dimensional closed W-quadratic Randers manifold is a Berwald manifold. In this paper, first we study the Riemann and Ricci curvatures of homogeneous Finsler manifolds and obtain some rigidity theorems. Then, by using this investigation, we construct a family of W-quadratic Randers metrics which are not R-quadratic nor strongly Ricci-quadratic.
DOI : 10.4153/S0008439524000493
Mots-clés : Flag curvature, Riemann curvature, Berwald curvature 
Tayebi, A. On Riemannian and Ricci curvatures of homogeneous Finsler manifolds. Canadian mathematical bulletin, Tome 68 (2025) no. 1, pp. 73-90. doi: 10.4153/S0008439524000493
@article{10_4153_S0008439524000493,
     author = {Tayebi, A.},
     title = {On {Riemannian} and {Ricci} curvatures of homogeneous {Finsler} manifolds},
     journal = {Canadian mathematical bulletin},
     pages = {73--90},
     year = {2025},
     volume = {68},
     number = {1},
     doi = {10.4153/S0008439524000493},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439524000493/}
}
TY  - JOUR
AU  - Tayebi, A.
TI  - On Riemannian and Ricci curvatures of homogeneous Finsler manifolds
JO  - Canadian mathematical bulletin
PY  - 2025
SP  - 73
EP  - 90
VL  - 68
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/S0008439524000493/
DO  - 10.4153/S0008439524000493
ID  - 10_4153_S0008439524000493
ER  - 
%0 Journal Article
%A Tayebi, A.
%T On Riemannian and Ricci curvatures of homogeneous Finsler manifolds
%J Canadian mathematical bulletin
%D 2025
%P 73-90
%V 68
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/S0008439524000493/
%R 10.4153/S0008439524000493
%F 10_4153_S0008439524000493

Cité par Sources :