Regularity of the geodesic equation in the space of Sasakian metrics

Details Regularity of the geodesic equation in the space of Sasakian metrics Regularity of the geodesic equation in the space of Sasakian metrics

2009-06-30

arxiv.org/abs/0906.5591v2

Mathematics

Differential Geometry

Scientific paper

This paper is devoted to the regularity analysis of a geodesic equation in the space of Sasakian metrics. Firstly, we reduce the geodesic equation in the space of Sasakian metrics to a Dirichlet problem of degenerate complex Monge-Amp\'ere type eqution on the K\"ahler cone; secondly, we obtain a priori etimates for the above equation. These a priori estimates guarantee the existence and uniqueness of $C^{2}_{w}$ geodesic for any two points in the space of Sasakian metrics. We also give some geometric applications of the above estimates in the end of this paper.

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