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.
Submitted January 2, 2017. Published July 5, 2017.
Math Subject Classifications: 53C44, 58J45, 58J47.
Key Words: Hyperbolic geometric flow; quasilinear hyperbolic equation; strict hyperbolicity.
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| Shahroud Azami |
Department of Mathematics, Faculty of Sciences
Imam Khomeini International University
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