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Kähler Metrics on the Projective Bundle of a Holomorphic Finsler Vector Bundle
- Source :
- Acta Mathematica Sinica, English Series. 36:1279-1291
- Publication Year :
- 2020
- Publisher :
- Springer Science and Business Media LLC, 2020.
-
Abstract
- Let (M,g) be a compact Kahler manifold and (E,F) be a holomorphic Finsler vector bundle of rank r ≥ 2over M. In this paper, we prove that there exists a Kahler metric Φ defined on the projective bundle P(E)of E, which comes naturally from g and F. Moreover, a necessary and sufficient condition for Φ having positive scalar curvature is obtained, and a sufficient condition for Φ having positive Ricci curvature is established.
- Subjects :
- Pure mathematics
Applied Mathematics
General Mathematics
010102 general mathematics
Holomorphic function
Vector bundle
Kähler manifold
Rank (differential topology)
01 natural sciences
Bundle
0103 physical sciences
Metric (mathematics)
Mathematics::Differential Geometry
010307 mathematical physics
0101 mathematics
Mathematics::Symplectic Geometry
Ricci curvature
Mathematics
Scalar curvature
Subjects
Details
- ISSN :
- 14397617 and 14398516
- Volume :
- 36
- Database :
- OpenAIRE
- Journal :
- Acta Mathematica Sinica, English Series
- Accession number :
- edsair.doi...........979a82b39589d1e8a3df961149aa5621