Frontiers of Mathematics in China >
Rotationally symmetric pseudo-Kähler-Einstein metrics
Received date: 30 Jan 2010
Accepted date: 18 Feb 2011
Published date: 01 Jun 2011
Copyright
In this paper, we construct some rotationally symmetric pseudo-Kähler-Einstein metrics on various holomorphic line bundles over projective spaces and their disc bundles. We also discuss the phase change phenomenon when one suitably changes parameters.
Xiaojuan DUAN , Jian ZHOU . Rotationally symmetric pseudo-Kähler-Einstein metrics[J]. Frontiers of Mathematics in China, 2011 , 6(3) : 391 -410 . DOI: 10.1007/s11464-011-0134-9
1 |
Calabi E. Métriques kählériennes et fibrés holomorphes. Annales Scientifiques de l’Ecole Normale Superieure, 1979, 12: 268-294
|
2 |
Calabi E. Extremal Kähler metrics. In: Yau S-T, ed. Seminars on Differential Geometry. Princeton: Princeton Univ Press and Univ of Tokyo Press, 1982, 259-290
|
3 |
Candelas P, de La Ossa XC. Comments on conifold. Nucl Phys, B, 1990, 342: 246-248
|
4 |
Cao H-D. Existence of gradient Kähler-Ricci solitons. In: Elliptic and Parabolic Methods in Geometry (Minneapolis, MN, 1994). Wellesley: A K Peters, 1996, 1-16
|
5 |
Feldman M, Ilmanen T, Knopf D. Rotationally symmetric shrinking and expanding gradient Kähler-Ricci solitons. J Diff Geom, 2003, 65: 169-209
|
6 |
Hwang A D, Singer M A. A momentum construction for circle-invariant Kähler metrics. Trans Amer Math Soc, 2002, 354: 2285-2325
|
7 |
Koiso N. On rotationally symmetric Hamilton’s equation for Kähler-Einstein metrics. In: Ochiai T, ed. Recent Topics in Differential and Analytic Geometry. Adv Stud Pure Math, 18-1. Tokyo and Boston: Kinokuniya and Academic Press, 1990.: 327-337
|
8 |
LeBrun C., Counter-examples to the generalized positive action conjecture. Comm Math Phys, 1988, 118: 591-596
|
9 |
Pedersen H, Poon Y S. Hamiltonian construction of Kähler-Einstein metrics and Kähler metrics of constant scalar curvature. Communications in Mathematical Physics, 1991, 136: 309-326
|
10 |
Simanca S R. Kähler metrics of constant scalar curvature on bundles over
|
11 |
Simanca S R. A note on extremal metrics of non-constant scalar curvature. Israel J Math, 1992, 78: 85-93
|
/
〈 | 〉 |