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Geodesics in the space of Kähler metrics
 
 
Description:  A Kähler manifold is a differentiable manifold with three geometric structures: a Riemannian metric, a symplectic form, and a complex structure, satisfying some compatibility conditions. The metrics and the symplectic forms for which these compatibility conditions are satisfied are called Kähler metrics and Kähler forms, respectively.
In this talk, we will show that, if we fix a complex structure on a compact Kähler manifold and if we choose a cohomology class for the Kähler forms, we can make the space of Kähler metrics into an infinite-dimensional manifold. Further, by giving this space the Mabuchi metric, we make it into a Riemannian manifold, for which we will study the geodesic equation. We will present an example of a geodesic curve in the case of the sphere. Time permitting, we will discuss how to obtain analytic solutions of the geodesic equation using an appropriate notion of complex flow.

 

Date:  2018-11-14
Start Time:   14:30
Speaker:  Pedro Silva (UC|UP PhD programme student)
Institution:  UC|UP PhD programme
Place:  Room 2.5, DMat of University of Coimbra
See more:   <Main>   <UC|UP MATH PhD Program>  
 
     
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