CNCS-UEFISCDI   ProJeCt PN-III-P1-1.1-PD-2021-0474

Starting date:  4th of January 2023

Ending date:  31st of December 2024

Budget: 250000 RON

Members: 

• Alexandra-Iulia Otiman   

• Vasile Brinzanescu (mentor)

Description of the project:

Prescribing special metrics on complex manifolds has seen broad developments over time, ranging from imposing special properties and symmetries to their holonomy groups or curvature tensors to considering maxima and minima in several variational problems. One modern approach to define special Hermitian metrics is to impose their fundamental form to be in the kernel of a specific differential operator. This is the case for locally conformally Kähler (lcK), balanced and pluriclosed metrics. This project regards the investigation of complex non-Kähler manifolds carrying the aforementioned type of metrics or special structures, such as tamed locally conformally symplectic. The two principal directions of research are: 1) finding new explicit examples of these metrics on manifolds that are strongly linked to number theory (such as Sankaran or Miebach-Oeljeklaus manifolds) and toric geometry (such as Kato toric manifolds) and 2) exploring their analytic and topological properties in relation to various types of cohomology (de Rham, Dolbeault, Bott-Chern). 

Papers:

1. D. Angella, A. Otiman, A note on compatibility of special Hermitian structures, arXiv:2306.02981

2. C. Ciulica, A. Otiman, M. Stanciu, Non-Kähler metrics on Endo-Pajitnov manifolds

Talks:

"Bott-Chern cohomology of compact Vaisman manifolds", Congress of the Romanian Mathematicians, Pitesti, June 2023