On Sinyukov’s Equations in Their Relation to a Curvature Operator of Second Kind

Abstract

AbstractMany authors have studied Riemannian manifolds admitting a geodesic mapping. Fundamental results of the theory of geodesic mapping were settled by Sinyukov. In the present paper we analyze the Sinykov equations of the geodesic mappings of Riemannian manifolds by using the curvature operator of the second kind. This approach to the study of geodesic mapping is essentially new.KeywordsRiemannian ManifoldOrthonormal BasisSectional CurvatureCurvature OperatorRicci TensorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.