|
|
New proof of a Calabi’s theorem |
Yingyi WU() |
School of Mathematical Sciences, Graduate University of Chinese Academy of Sciences, Beijing 100049, China |
|
|
Abstract A Calabi’s theorem says that on a compact Riemann surface, an extremal metric is a constant scalar curvature metric. In this paper, we use a new method to prove this theorem. Then we give an interesting corollary.
|
Keywords
Extremal metric
compact Riemann surface
|
Corresponding Author(s):
WU Yingyi,Email:Chinawuyy@gucas.ac.cn
|
Issue Date: 01 October 2012
|
|
1 |
Calabi E. Extremal K?hler metrics. In: Yau S T, ed. Seminar on Differential Geometry. Ann Math Stud, 102 . Princeton: Princeton Univ Press, 1982, 259-290
|
2 |
Chen Q, Wu Y Y. Existences and explicit constructions of HCMU metrics on S2 and T2. Pacific J Math , 2009, 240(2): 267-288 doi: 10.2140/pjm.2009.240.267
|
3 |
Chen Q, Wu Y Y. Character 1-form and the existence of an HCMU metric. Math Ann , 2011, 351(2): 327-351 doi: 10.1007/s00208-010-0598-z
|
4 |
Chen X X. Obstruction to the existence of metric whose curvature has umbilical Hessian in a K-Surface. Comm Anal Geom , 2000, 8(2): 267-299
|
5 |
Lin C S, Zhu X H. Explicit construction of extremal Hermitian metric with finite conical singularities on S2. Comm Anal Geom , 2002, 10(1): 177-216
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
|
Shared |
|
|
|
|
|
Discussed |
|
|
|
|