Hyperbolic Ricci-Bourguignon-Harmonic Flow

Abstract

In this paper, we consider hyperbolic Ricci-Bourguignon flow on a compact Riemannian manifold M coupled with the harmonic map flow between M and a fixed manifold N. At the first, we prove the unique short-time existence to solution of this system. Then, we find the second variational of some geometric structure of M along this system such as, curvature tensors. In addition, for emphasize the importance of hyperbolic Ricci-Bourguignon flow, we give some examples of this flow on Riemannian manifolds.

Keywords

• ricci flow
• hyperbolic equation
• harmonic map
• strictly hyperbolicity