Research

Outline: 

In 1958 K. Kodaira and D. C. Spencer proved that the Kaehler property is open under holomorphic deformations  (This paper). Since then, similar questions have arisen for metrics such as balanced, SKT, H-s, Gauduchon, etc. Some of them are answered, but some are not. My line of research is based on the Kodaira-Spencer theory on the Deformations of Complex Analytic Structures. My main interest is investigating whether a geometric property is open (closed) under holomorphic deformations. 

I am currently working on the existence of an l.c.K metric on a compact complex manifold and other complex structures on an L.c.K manifold. For example, can an l.c.K (locally conformally Kaehler) manifold admit an SKT (strong Kaehler with torsion) metric? 

Paper :

1. E. Soheil - Properties of Critical Points of the Dinew-Popovici Energy Functional,  Journal of Complex Manifolds, vol (9) 202. Link. (PDF) 

2. D. Popovici, E. Soheil, Functionals for the Study of LCK Metrics on Compact Complex Manifolds. Bulletin des sciences mathématiques, 188 (2023) 103319. (PDF)

Talks :

• Functionals for the Study of LCK Metrics on Compact Complex Manifolds, Torino, Italy 18 May, 2023. 

• Hermitian-Symplectic Manifolds and Dinew-Popovici Functiona, the Dynamical Systems and Geometry seminar, University of Angers. 23 May 2023.

• Séminaire QUID, Quid of special metrics on a compact complex manifold?, IMT, March 2023.