Weak Metric Structures on Generalized Riemannian Manifolds, Weak Metric Structures on Generalized Riemannian Manifolds, ICMS seminar talk by Milan Zlatanovic
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 rank(F)= dim M and non-conformal tensor A2, 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 A2. For rank(F)< dim M we apply weak f-structures and obtain splitting results for generalized Riemannian manifolds.
