Publication details
Invariant connections and Nabla-Einstein structures on isotropy irreducible spaces
| Authors | |
|---|---|
| Year of publication | 2019 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Geometry and Physics |
| MU Faculty or unit | |
| Citation | |
| Web | Full Text |
| Doi | http://dx.doi.org/10.1016/j.geomphys.2018.10.012 |
| Keywords | Homogeneous space; Connection; Symmetric space; Irreducible; Isotropy |
| Description | This paper is devoted to a systematic study and classification of invariant affine or metric connections on certain classes of naturally reductive spaces. For any non-symmetric, effective, strongly isotropy irreducible2homogeneous Riemannian manifold , we compute the dimensions of the spaces of -invariant affine and metric connections. For such manifolds we also describe the space of invariant metric connections with skew-torsion. For the compact Lie group we classify all bi-invariant metric connections, by introducing a new family of bi-invariant connections whose torsion is of vectorial type. Next we present applications related with the notion of -Einstein manifolds with skew-torsion. In particular, we classify all such invariant structures on any non-symmetric strongly isotropy irreducible homogeneous space. |