Calamai, Simone, Petrecca, David and Zheng, Kai (2016) The geodesic problem for the Dirichlet metric and the Ebin metric on the space of Sasakian metrics. New York Journal of Mathematics , 22 . pp. 1111-1133. ISSN 1076-9803.
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Abstract
We study the geodesic equation for the Dirichlet (gradient) metric in the space of Kähler potentials. We first solve the initial value problem for the geodesic equation of the combination metric, including the gradient metric. We then discuss a comparison theorem between it and the Calabi metric. As geometric motivation of the combination metric, we find that the Ebin metric restricted to the space of type II deformations of a Sasakian structure is the sum of the Calabi metric and the gradient metric.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics |
| Library of Congress Subject Headings (LCSH): | Geodesics (Mathematics), Cauchy problem |
| Journal or Publication Title: | New York Journal of Mathematics |
| Publisher: | College of Arts and Sciences * University at Albany |
| ISSN: | 1076-9803 |
| Official Date: | 23 September 2016 |
| Dates: | Date Event 23 September 2016 Published 24 August 2016 Accepted |
| Volume: | 22 |
| Page Range: | pp. 1111-1133 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| Date of first compliant deposit: | 20 November 2017 |
| Date of first compliant Open Access: | 20 November 2017 |
| RIOXX Funder/Project Grant: | Project/Grant ID RIOXX Funder Name Funder ID EP/K00865X/1 Engineering and Physical Sciences Research Council |
| Related URLs: | |
| URI: | https://wrap.warwick.ac.uk/94840/ |
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