University of Kashan Mathematics Interdisciplinary Research 2538-3639 7 1 2022 03 01 Hyperbolic Ricci-Bourguignon-Harmonic Flow 61 76 111935 10.22052/mir.2021.240451.1272 EN Shahrood Azami Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran Journal Article 2021 01 27 In this paper, we consider hyperbolic Ricci-Bourguignon flow on a compact Riemannian manifold <em>M</em> coupled with the harmonic map flow between <em>M</em> and a fixed manifold <em>N</em>. 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 <em>M</em> 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. Ricci flow Hyperbolic equation Harmonic map Strictly hyperbolicity https://mir.kashanu.ac.ir/article_111935_76f6751f8d6e1babca74174d0feb9684.pdf