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Commun. Korean Math. Soc. 2023; 38(2): 575-588
Online first article December 6, 2022 Printed April 30, 2023
https://doi.org/10.4134/CKMS.c220112
Copyright © The Korean Mathematical Society.
Generalized hyperbolic geometric flow
Shahroud Azami, Ghodratallah Fasihi~Ramandi, Vahid Pirhadi
Imam Khomeini International University; Imam Khomeini International University; University of Kashan
In the present paper, we consider a kind of generalized hyperbolic geometric flow which has a gradient form. Firstly, we establish the existence and uniqueness for the solution of this flow on an $n$-dimensional closed Riemannian manifold. Then, we give the evolution of some geometric structures of the manifold along this flow.
Keywords: Hyperbolic geometric flow, quasilinear hyperbolic equation, strict hyperbolicity
MSC numbers: Primary 53E22, 58J45, 58J47
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