Connections on non-symmetric (generalized) Riemannian manifold and gravity

摘要: Connections with (skew-symmetric) torsion on non-symmetric Riemannian manifold satisfying the Einstein metricity condition (NGT torsion) are considered. It is shown that an almost Hermitian NGT if and only it a Nearly K\"ahler manifold. In case of contact metric spaces characterized possibly new class manifolds extracted. Similar considerations lead to definition particular classes para-Hermitian paracontact manifolds. The conditions given in terms corresponding Nijenhuis tensors exterior derivative skew-symmetric part metric.