##### Department of Mathematics,

University of California San Diego

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### Math 248 - Analysis Seminar

## Keegan Flood

#### University of Aukland

## C-projective metrizability and CR submanifolds

##### Abstract:

The c-projective metrizability equation is an invariant overdetermined linear geometric PDE on an almost c-projective manifold governing the existence of quasi-Kahler metrics compatible with the c-projective structure. I will show that the degeneracy locus of a solution to the c-projective metrizability equation satisfying a generic condition on its prolonged system is a smoothly embedded submanifold of codimension 1 which inherits a partially-integrable nondegenerate almost CR structure. Phrased differently, this result explicitly links the Levi-form of the boundary CR structure of a c-projectively compact quasi-Kahler manifold satisfying a non-vanishing 'generalized scalar curvature' condition to the interior metric.

Hosts: Peter Ebenfelt and Sean Curry

### May 7, 2019

### 2:00 PM

### AP&M 7218

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