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Generalized hyperbolic geometric flow

Shahroud Azami|Ghodratallah Fasihi-Ramandi|Vahid Pirhadi
대한수학회 (The Korean Mathematical Society)|2023.04|대한수학회논문집 (Communications of the KMS)|제38권 제2호|pp. 575-588|DOI 10.4134/CKMS.c220112

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키워드

Hyperbolic geometric flowquasilinear hyperbolic equationstrict hyperbolicity
주제분류수학

초록

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.

Abstract

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.

참고문헌 (13)

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  2. S. Azami, "Ricci-Bourguignon flow coupled with harmonic map flow", Internat. J. Math, 30(10), pp.1950049~1950065 (2019)[DOI]
  3. S. Azami, "Hyperbolic Ricci-Bourguignon flow", Comput. Methods Differ. Equ, 9(2), pp.399~409 (2021)[DOI]
  4. J. -P. Bourguignon, "Ricci curvature and Einstein metrics, in Global differential geometry and global analysis (Berlin, 1979)", Lecture Notes in Math, 838, pp.42~63 (1981), Springer
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  6. B. Chow, "The Ricci flow: An Introduction, Mathematical Surveys and Monographs, 110" (2004), American Mathematical Society
  7. W. -R. Dai, "Hyperbolic geometric flow(I) : short-time existence and nonlinear stability", Pure Appl. Math. Q, 6(2, Special Issue: In honor of Michael Atiyah and Isadore Singer), pp.331~359 (2010)[DOI]
  8. D. M. DeTurck, "Deforming metrics in the direction of their Ricci tensors", J. Differential Geom, 18(1), pp.157~162 (1983)[DOI]
  9. R. S. Hamilton, "Three-manifolds with positive Ricci curvature", J. Differential Geometry, 17(2), pp.255~306 (1982)[DOI]
  10. D. -X. Kong, "Wave character of metrics and hyperbolic geometric flow", J. Math. Phys, 48(10), pp.103508~103521 (2007)[DOI]
  11. B. List, "Evolution of an extended Ricci flow system", Comm. Anal. Geom, 16(5), pp.1007~1048 (2008)[DOI]
  12. R. M¨uller, "Ricci flow coupled with harmonic map flow", Ann. Sci. ´Ec. Norm. Sup´er. (4), 45(1), pp.101~142 (2012)[DOI]
  13. Jia-Yong Wu, "A general Ricci flow system", 대한수학회지, 55(2), pp.253~292 (2018), 대한수학회

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