HOMOTHETIES AND PARALLEL TRANSLATIONS IN PROJECTIVE SYMMETRIC SPACES OF AFFINE CONNECTION
The paper deals with the algebraic and geometric properties of a broad class of projective symmetric affine-connected manifolds with a nonzero torsion tensor field having common homotheties with symmetric spaces. Such spaces are called prosimmetric. Various subclasses of these spaces are discussed. We study the properties of parallel translations and homotheties from the viewpoint of differentiable unassociative universal algebras. The necessary and sufficient algebraic conditions, which a geodesic loop satisfies at each point in a prosimmeric manifold with affine connection, are obtained.