The aim is to characterize the nature of lie groups with a left invariant Riemannian metric and flat connections with skew-symmetric torsion.
Descriptive analysis of geometric properties of lie groups.
Examination of the relationship between left invariant Riemannian metrics and flat connections.
Identification of conditions for skew-symmetric torsion.
Comprehensive classification of relevant lie groups is provided.
Identification of invariant properties under certain geometric conditions is demonstrated.
Abstract
We give a complete description of Lie groups endowed with a left invariant Riemannian metric and a left invariant flat metric connection with skew-symmetric torsion.