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arXiv · 0906.5591

Regularity of the geodesic equation in the space of Sasakian metrics

PengFei Guan·Xi Zhang
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Abstract

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-Ampére type eqution on the Kähler 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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PengFei Guan, Xi Zhang. 2009-07-29. Regularity of the geodesic equation in the space of Sasakian metrics. https://arxiv.org/abs/0906.5591

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