
Rotationally symmetric pseudo-K?hler-Einstein metrics
Xiaojuan DUAN, Jian ZHOU
Front. Math. China ›› 2011, Vol. 6 ›› Issue (3) : 391-410.
Rotationally symmetric pseudo-K?hler-Einstein metrics
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.
Rotationally symmetric / pseudo-Kähler-Einstein metrics / phase change
[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
CrossRef
Google scholar
|
[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
CrossRef
Google scholar
|
[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
CrossRef
Google scholar
|
[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
CrossRef
Google scholar
|
[10] |
Simanca S R. Kähler metrics of constant scalar curvature on bundles over
CrossRef
Google scholar
|
[11] |
Simanca S R. A note on extremal metrics of non-constant scalar curvature. Israel J Math, 1992, 78: 85-93
CrossRef
Google scholar
|
/
〈 |
|
〉 |