Hyperbolic Ricci-Bourguignon flow

In this paper, we consider the hyperbolic Ricci-Bourguignon flow on a compact manifold M and show that this flow has a unique solution on short-time with imposing on initial conditions. After then, we find evolution equations for Riemannian curvature tensor, Ricci curvature tensor and scalar curvature of M under this flow. In the final section, we give some examples of this flow on some compact manifolds.

Hyperbolic Ricci-Bourguignon flow Keywords:

Geometric flow , Hyperbolic equation , Strictly hyperbolicity