hyperbolic ricci-bourguignon-harmonic flow

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.