ON PROJECTIVE SYMMETRIC ZERO CURVATURE MANIFOLDS WITH AFFINE CONNECTION

Abstract

The paper deals with the geometric properties of the zero curvature manifolds with affine connection having common geodesic lines with preservation of the affine (canonical) parameter with locally symmetric spaces of affine connectivity. This class of spaces is characterized by identities satisfied by the torsion tensor field and its covariant derivatives. Geodesic loops with homotheties of this class of affine connected manifolds are investigated.

Keywords

• manifolds with affine connection of zero curvature
• symmetric spaces with affine connection
• a geodesic loop
• parallel translations
• homothety