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.

On the geodesic problem for the Dirichlet metric and the Ebin metric on the space of Sasakian metrics / Calamai, Simone; Petrecca, David; Zheng, Kai. - In: NEW YORK JOURNAL OF MATHEMATICS. - ISSN 1076-9803. - ELETTRONICO. - 22:(2016), pp. 1111-1133.

On the geodesic problem for the Dirichlet metric and the Ebin metric on the space of Sasakian metrics

CALAMAI, SIMONE;
2016

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.
2016
22
1111
1133
Calamai, Simone; Petrecca, David; Zheng, Kai
File in questo prodotto:
File Dimensione Formato  
1405.1211.pdf

accesso aperto

Tipologia: Preprint (Submitted version)
Licenza: Open Access
Dimensione 269.73 kB
Formato Adobe PDF
269.73 kB Adobe PDF

I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1055082
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact