On July 15, 2025, at 1:00 pm in Room 403 there will be a joint seminar of the Analysis, Geometry and Topology Department and the International Center for Mathematical Sciences – Sofia (ICMS-Sofia).

A talk on:

Weak Metric Structures on Generalized Riemannian Manifolds

will be delivered by Milan Zlatanovic, University of Niš, Serbia.

Abstract. Linear connections with torsion are important in the study of generalized Riemannian manifolds (\(M\), \(G=g+F\)), where the symmetric part \(g\) of \(G\) is a non-degenerate (0,2)-tensor and \(F\) is the skew-symmetric part. Some space-time models in theoretical physics are based on \((M, G=g+F)\), where \(F\) is defined using a complex structure. In the lecture, we will show more general models, where \(F\) has constant rank and is based on weak metric structures (introduced by the V. Rovenski and R. Wolak), which generalize almost contact and \(f\)-contact structures. We consider metric connections (i.e., preserving \(G\)) with totally skew-symmetric torsion tensor. For \(\mbox{rank}(F)= \mbox{dim} M\) and non-conformal tensor \(A^2\), where \(A\) is a skew-symmetric (1,1)-tensor adjoint to \(F\), we apply weak almost Hermitian structures to fundamental results (by S. Ivanov and M. Zlatanovic) on generalized Riemannian manifolds and prove that the manifold is a weighted product of several nearly Kahler manifolds corresponding to eigen-distributions of \(A^2\). For \(\mbox{rank}(F)< \mbox{dim} M\) we apply weak \(f\)-structures and obtain splitting results for generalized Riemannian manifolds.
(This is joint work with Vladimir Rovenski, Department of Mathematics, University of Haifa).

The lecturer’s visit is supported by the Scientific Programme “Enhancing the Research Capacity in Mathematical Sciences (PIKOM)”.