Conformal geometry of Riemannian submanifolds Gauss, Codazzi and Ricci equations

Abstract

Let f : (N,g) → (N, g¯) be a conformal immersion of Riemannian manifolds. We establish a relation between the Weyl tensor of N and the Weyl tensor of the restriction to N of the curvature tensor of N. Such relation is invariant for conformal changes of the metrics of N and N. An application to the locally conformal Kahler manifolds is given. If f is an isometry we prove that Ricci equation of N, as submanifold of N, is invariant under conformal changes of the metric of N. The analogous of Codazzi equation, in conformal geometry, is found.

Keywords

• equazioni di gauss codazzi ricci
• immersioni conformi
• varietà localmente conformemente hahalerian