# American Institute of Mathematical Sciences

• Previous Article
Blowup of solutions to the thermal boundary layer problem in two-dimensional incompressible heat conducting flow
• CPAA Home
• This Issue
• Next Article
Sharp Hardy-Leray inequality for three-dimensional solenoidal fields with axisymmetric swirl
June  2020, 19(6): 3223-3231. doi: 10.3934/cpaa.2020140

## Ricci curvature of conformal deformation on compact 2-manifolds

 Department of Mathematics, Chosun University, Kwangju, 61452, Republic of Korea

* Corresponding author

Received  June 2019 Revised  December 2019 Published  March 2020

Fund Project: The first author was supported by Chosun University Research Fund 2018

In this paper, we consider Ricci curvature of conformal deformation on compact 2-manifolds. And we prove that, by the conformal deformation, the resulting manifold is an Einstein manifold.

Citation: Yoon-Tae Jung, Soo-Young Lee, Eun-Hee Choi. Ricci curvature of conformal deformation on compact 2-manifolds. Communications on Pure & Applied Analysis, 2020, 19 (6) : 3223-3231. doi: 10.3934/cpaa.2020140
##### References:
 [1] T. Aubin, Nonlinear Analysis on Manifolds, Springer-Verlag, New York, 1982.  Google Scholar [2] M. S. Berger, Riemannian structures of prescribed Gaussian curvature for compact 2-manifolds, J. Differ. Geom., 5 (1971), 325-332.   Google Scholar [3] A. L. Besse, Einstein Manifolds, Springer-Verlag, New York, 1987. doi: 10.1007/978-3-540-74311-8.  Google Scholar [4] H. Ge and W. Jiang, Kazdan-Warner equation on infinite graph, J. Korean Math. Soc., 55 (2018), 1091-1101.  doi: 10.4134/JKMS.j170561.  Google Scholar [5] J. L. Kazdan and F. W. Warner, Curvature functions for compact 2-manifolds, Ann. Math., 99 (1974), 14-47.  doi: 10.2307/1971012.  Google Scholar [6] B. O'Neill, Semi-Riemannian Geometry, Academic, New York, 1983.  Google Scholar [7] R. Walter, Real and Complex Analysis, McGraw-Hill, Singapore, 1986. Google Scholar

show all references

##### References:
 [1] T. Aubin, Nonlinear Analysis on Manifolds, Springer-Verlag, New York, 1982.  Google Scholar [2] M. S. Berger, Riemannian structures of prescribed Gaussian curvature for compact 2-manifolds, J. Differ. Geom., 5 (1971), 325-332.   Google Scholar [3] A. L. Besse, Einstein Manifolds, Springer-Verlag, New York, 1987. doi: 10.1007/978-3-540-74311-8.  Google Scholar [4] H. Ge and W. Jiang, Kazdan-Warner equation on infinite graph, J. Korean Math. Soc., 55 (2018), 1091-1101.  doi: 10.4134/JKMS.j170561.  Google Scholar [5] J. L. Kazdan and F. W. Warner, Curvature functions for compact 2-manifolds, Ann. Math., 99 (1974), 14-47.  doi: 10.2307/1971012.  Google Scholar [6] B. O'Neill, Semi-Riemannian Geometry, Academic, New York, 1983.  Google Scholar [7] R. Walter, Real and Complex Analysis, McGraw-Hill, Singapore, 1986. Google Scholar
 [1] Huyuan Chen, Dong Ye, Feng Zhou. On gaussian curvature equation in $\mathbb{R}^2$ with prescribed nonpositive curvature. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3201-3214. doi: 10.3934/dcds.2020125 [2] Buddhadev Pal, Pankaj Kumar. A family of multiply warped product semi-Riemannian Einstein metrics. Journal of Geometric Mechanics, 2020, 12 (4) : 553-562. doi: 10.3934/jgm.2020017 [3] Wenjun Liu, Yukun Xiao, Xiaoqing Yue. Classification of finite irreducible conformal modules over Lie conformal algebra $\mathcal{W}(a, b, r)$. Electronic Research Archive, , () : -. doi: 10.3934/era.2020123 [4] Editorial Office. Retraction: Xiaohong Zhu, Zili Yang and Tabharit Zoubir, Research on the matching algorithm for heterologous image after deformation in the same scene. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1281-1281. doi: 10.3934/dcdss.2019088 [5] Petr Pauš, Shigetoshi Yazaki. Segmentation of color images using mean curvature flow and parametric curves. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1123-1132. doi: 10.3934/dcdss.2020389 [6] Kohei Nakamura. An application of interpolation inequalities between the deviation of curvature and the isoperimetric ratio to the length-preserving flow. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1093-1102. doi: 10.3934/dcdss.2020385 [7] Tetsuya Ishiwata, Takeshi Ohtsuka. Numerical analysis of an ODE and a level set methods for evolving spirals by crystalline eikonal-curvature flow. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 893-907. doi: 10.3934/dcdss.2020390

2019 Impact Factor: 1.105