Harmonic-hyperbolic geometric flow

Abstract

In this article we study a coupled system for hyperbolic geometric flow on a closed manifold M, with a harmonic flow map from M to some closed target manifold N. Then we show that this flow has a unique solution for a short-time. After that, 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 closed manifolds.

Keywords

• Hyperbolic geometric flow
• quasilinear hyperbolic equation
• strict hyperbolicity