##### Department of Mathematics,

University of California San Diego

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### Math 258 - Seminar/Differential Geometry

## Dan Popovici

#### University of Toulouse

## Hermitian-symplectic and K\"ahler Metrics on Compact Complex Manifolds"

##### Abstract:

This is joint work with S. Dinew (Krakow). We investigate the class of compact complex Hermitian-symplectic manifolds $X$. For each Hermitian-symplectic metric $\omega$ on $X$, we introduce a functional acting on the metrics in a certain cohomology class of $\omega$ and prove that its critical points (if any) must be K\"ahler when X is 3-dimensional.

Host: Peter Ebenfelt

### November 29, 2021

### 10:00 AM

### Zoom: https://ucsd.zoom.us/j/98902196321

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