Moser Vector Fields and Geometry of the Mabuchi Moduli Space of Kähler Metrics
Author
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-01-02
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
There is a natural Moser type transformation along any curve in the moduli spaces of Kähler metrics.
In this paper we apply this transformation to give an explicit construction of the parallel transformation along a curve in the Mabuchi moduli space of Kähler metrics.
This is crucial in the proof of the equivalence between the existence of the Kähler metrics with constant scalar curvature and the geodesic stability for the type II compact almost homogeneous manifolds of cohomogeneity one mentioned in (Guan 2013).
We also explain a new description of the geodesics and prove a curvature property of the moduli space, called curvature symmetric, which makes it similar to some special symmetric spaces with nonpositive curvatures, although the spaces are usually not complete.
Finally, we generalize our geodesic stability conjectures in (Guan 2003) and give several results on the Lie algebra structures related to the parallel transformations.
In the last section, we generalize the Futaki obstruction of the Kähler-Einstein metrics to the parallel vector fields of the invariant Mabuchi moduli space.
We call the related stability the parallel stability.
This includes the toric and cohomogeneity one cases as well as the spherical manifolds.
American Psychological Association (APA)
Guan, Daniel. 2014. Moser Vector Fields and Geometry of the Mabuchi Moduli Space of Kähler Metrics. Geometry،Vol. 2014, no. 2014, pp.1-6.
https://search.emarefa.net/detail/BIM-512176
Modern Language Association (MLA)
Guan, Daniel. Moser Vector Fields and Geometry of the Mabuchi Moduli Space of Kähler Metrics. Geometry No. 2014 (2014), pp.1-6.
https://search.emarefa.net/detail/BIM-512176
American Medical Association (AMA)
Guan, Daniel. Moser Vector Fields and Geometry of the Mabuchi Moduli Space of Kähler Metrics. Geometry. 2014. Vol. 2014, no. 2014, pp.1-6.
https://search.emarefa.net/detail/BIM-512176
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-512176