Complex and Riemannian Geometry and their Applications
Project number: KP-06-Н82/6
Base organization:
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences
Project leader:
Prof. PhD Velichka Milousheva
Funding:
Bulgarian National Science Fund, Competition for financial support of basic research projects – 2024
Period:
December 2024 – December 2027
Team:
Prof. PhD Velichka Milousheva
IMI-BAS
Corr. Member of BAS Prof. D.Sc. Nikolai Nikolov
IMI-BAS
Assist. Prof. PhD Maria Trybula
Adam Mickiewicz University in Poznan and IMI-BAS
Chief Assist. Prof. PhD Victoria Bencheva
IMI-BAS and VTU “St. St. Cyril and Methodius”
Prof. D.Sc. Johann Davidov
IMI-BAS
Prof. PhD Ognian Kassabov
IMI-BAS
Research plan:
Work package 1.
Analytic and geometric problems in several complex variables
Work package 2.
Geometry of generalized twistor spaces
Work package 3.
The problem of Lund-Regge for surfaces in 4-dimensional pseudo-Euclidean spaces
Expected results:
- Finding an optimal regularity of the boundary of a domain in Cn for which Kobayashi visibility implies pseudoconvexity.
- A representation of bounded linear operators between spaces of holomorphic functions for certain classes of domains in Cn via germs of holomorphic functions.
- Establishing the possible Gray-Hervella classes of natural almost Hermitian structures on a generalized twistor space.
- Obtaining a coordinate-free formula for the curvature of a natural Riemannian metric on а generalized twistor space and finding conditions on the base manifold for this metric to be Einstein.
- Finding conditions on two generalized Riemannian metrics on a manifold under which the generalized twistor spaces determined by these metrics “coincide “, i.e. are equivalent in a suitable sense, when considering with their generalized almost complex structures.
- Describing the class of marginally trapped (quasi-minimal) surfaces in terms of minimal number of partial differential equations.
- Introducing special uniquely determined parameters on surfaces in the Euclidean 4-space that allow the reduction of the number of PDEs determining the surfaces.
- Introducing special isotropic parameters on Lorentz surfaces with parallel normalized mean curvature vector field in the pseudo-Euclidean 4-space with neutral metric and solving the Lund-Regge problem.
- Construction of meridian timelike surfaces in the Minkowski 4-space and investigation of their basic invariants.
