Rotationally symmetric pseudo-Kähler-Einstein metrics

Abstract

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.

Keywords

Rotationally symmetric / pseudo-Kähler-Einstein metrics / phase change

References

[1] Calabi E. Métriques kählériennes et fibrés holomorphes. Annales Scientifiques de l’Ecole Normale Superieure, 1979, 12, 268-294

[2] Calabi E. Yau S.-T. Extremal Kähler metrics. Seminars on Differential Geometry, 1982, Princeton: Princeton Univ Press and Univ of Tokyo Press 259-290

[3] Candelas P., de La Ossa X.C. Comments on conifold. Nucl Phys, B, 1990, 342, 246-248

[4] Cao H. -D. Existence of gradient Kähler-Ricci solitons. Elliptic and Parabolic Methods in Geometry (Minneapolis, MN, 1994), 1996, Wellesley: A K Peters 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. Ochiai T. On rotationally symmetric Hamilton’s equation for Kähler-Einstein metrics. Recent Topics in Differential and Analytic Geometry. Adv Stud Pure Math, 18-1, 1990, Tokyo and Boston: Kinokuniya and Academic Press 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 CP _n−1. Math Ann, 1991, 291, 239-246

[11] Simanca S. R. A note on extremal metrics of non-constant scalar curvature. Israel J Math, 1992, 78, 85-93