| Title:
|
Some rigidity theorems for Finsler manifolds of sectional flag curvature (English) |
| Author:
|
Wu, Bing Ye |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
46 |
| Issue:
|
2 |
| Year:
|
2010 |
| Pages:
|
99-104 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we study some rigidity properties for Finsler manifolds of sectional flag curvature. We prove that any Landsberg manifold of non-zero sectional flag curvature and any closed Finsler manifold of negative sectional flag curvature must be Riemannian. (English) |
| Keyword:
|
Finsler manifold |
| Keyword:
|
Landsberg manifold |
| Keyword:
|
scalar flag curvature |
| Keyword:
|
sectional flag curvature |
| Keyword:
|
Cartan tensor |
| MSC:
|
53B40 |
| MSC:
|
53C60 |
| idZBL:
|
Zbl 1240.53131 |
| idMR:
|
MR2684252 |
| . |
| Date available:
|
2010-06-22T22:11:19Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140306 |
| . |
| Reference:
|
[1] Akbar-Zadeh, H.: Sur les espaces de Finsler à courbures sectionnelles constantes.Acad. Roy. Belg. Bull. Cl. Sci. (6) 74 (1988), 281–322. Zbl 0686.53020, MR 1052466 |
| Reference:
|
[2] Chen, B., Zhao, L. L.: Randers metrics of sectional flag curvature.Houston J. Math., to appear. MR 2610781 |
| Reference:
|
[3] Chen, X., Mo, X., Shen, Z.: On the flag curvature of Finsler metrics of scalar curvature.J. London Math. Soc. 68 (2003), 762–780. Zbl 1063.53078, MR 2010010, 10.1112/S0024610703004599 |
| Reference:
|
[4] Chern, S. S.: Local equivalence and Euclidean connections in Finsler spaces.Sci. Rep. Nat. Tsing Hua Univ. Ser. A5 (1948), 95–121, or Selected Papers, II, 194-212, Springer 1989. Zbl 0200.00004, MR 0031812 |
| Reference:
|
[5] Chern, S. S., Shen, Z.: Riemannian-Finsler geometry.World Sci., Singapore, 2005. MR 2169595 |
| Reference:
|
[6] Mo, X.: The flag curvature tensor on a closed Finsler spaces.Res. Math. 36 (1999), 149–159. MR 1706528, 10.1007/BF03322108 |
| Reference:
|
[7] Numata, S.: On Landsberg spaces of scalar curvature.J. Korean Math. Soc. 12 (1975), 97–100. Zbl 0314.53017, MR 0402643 |
| . |
