Zhuangdan Guan . MAXWELL-EINSTEIN METRICS ON COMPLETIONS OF CERTAIN ${\bf C}^*$ BUNDLES^*[J]. Acta mathematica scientia, Series B, 2023 , 43(1) : 363 -372 . DOI: 10.1007/s10473-023-0120-9

[1] Apostolov V, Maschler G.Conformally Kähler Einstein-Maxwell geometry. J Eur Math Soc, 2019, 21(5): 1319-1360
[2] Apostolov V, Maschler G, Tonnesen-Friedman C.Weighted extremal Kähler metrics and the Einstein- Maxwell geometry of projective bundles. arXiv:1808.02813
[3] Aubin T.Nonlinear Analysis on Manifolds, Monge-Amp`ere Equations. New York, Heidelberg Berlin: Springer-Verlag, 1982
[4] Calabi E.Extremal Kähler metrics. Annals of Math Studies, 1982, 102: 259-290
[5] Calabi E.Extremal Kähler metrics II//Differential Geometry and Complex Analysis. Springer-Verlag, 1985: 95-114
[6] Chen B, Zhu X.Yau’s uniformization conjecture for manifolds with non-maximal volume growth. Acta Mathematica Scientia, 2018, 38B(5): 1468-1484
[7] Derdzinski A.Self-dual Kähler manifolds and Einstein manifolds of dimension four. Compositio Math, 1983, 49: 405-433
[8] Druet O.Nonlinear Analysis on Manifolds. 2005
[9] Duan X, Guan D.Complete Kähler metrics with positive holomorphic sectional curvatures on certain line bundles and a cohomogeneity one point of view on a Yau conjecture. Preprint, 2022
[10] Futaki A, Mabuchi T.Bilinear forms and extremal Kähler vector fields associated with Kähler classes. Math Ann, 1995, 301: 199-210
[11] Futaki A, Mabuchi T, Sakane Y.Einstein-Kähler metrics with positive Ricci curvature//Recent Topics in Complex Geometry. Adv Studies in Pure Math, 18-I. Academic Press, 1989: 1-73
[12] Futaki A, Ono H.Volume minimization and conformally Kähler, Einstein-Maxwell geometry. J Math Soc Japan, 2018, 70(4): 1493-1521
[13] Futaki A, Ono H.Conformally Einstein-Maxwell Kähler metrics and structure of the automorphism group. Math Z, 2019, 292(1/2): 571-589
[14] Guan D, Chen X.Existence of extremal metrics on almost homogeneous manifolds of cohomogeneity one. Asian J Math, 2000, 4: 817-830
[15] Guan Z.On Certain Complex Manifolds[D]. University of California, at Berkeley. Spring, 1993
[16] Guan Z.Existence of extremal metrices on compact almost homogeneous manifolds with two ends. Trans Amer Math Soc, 1995, 347: 2255-2262
[17] Guan Z.Quasi-Einstein metrics. International J Math, 1995, 6(3): 371-379
[18] Guan D.On modified Mabuchi functional and Mabuchi moduli space of Kähler metrics on toric bundles. Math Res Lett, 1999, 6: 547-555
[19] Guan D.Existence of extremal metrics on almost homogeneous manifolds of cohomogeneity one—III. Intern J Math, 2003, 14: 259-287
[20] Hwang A, Simanca S.Distinguished Kähler metrics on Hirzebruch surfaces. Trans Amer Math Soc, 1995, 347(3): 1013-1021
[21] Hwang A, Simanca S.Extremal Kähler metrics on Hirzebruch surfaces which are locally conformally equivalent to Einstein metrics. Math Ann, 1997, 309(1): 97-106
[22] Huckleberry A, Snow D.Almost-homogeneous Kähler manifolds with hypersurface orbits. Osaka J Math, 1982, 19: 763-786
[23] Kobayashi S.Differential Geometry of Complex Vector Bundles. Iwanami Shoten Publishers and Princeton University Press, 1987
[24] Koiso N.On rotationally symmetric Hamilton’s equations for Kähler-Einstein metrics. Max-Planck-Institut preprint series, 1987: 87-16
[25] Koiso N.On rotationally symmetric Hamilton’s equations for Kähler-Einstein metrics//Adv Studies Pure Math 18-I. Academic Press, 1990: 327-337
[26] Koiso N, Sakane Y.Non-homogeneous Kähler-Einstein metrics on compact complex manifolds//Lecture Notes in Math 1201. Springer, 1986: 165-179
[27] Koiso N, Sakane Y.Non-homogeneous Kähler-Einstein metrics on compact complex manifolds II. Osaka J Math, 1988, 25: 933-959
[28] LeBrun C. The Einstein-Maxwell equations, Kähler metrics, and Hermitian geometry. J Geom Phys, 2015, 91: 163-171
[29] LeBrun C. The Einstein-Maxwell equations and conformally Kähler geometry. Comm Math Phys, 2016, 344(2): 621-653
[30] Mabuchi T.Einstein-Kähler forms, Futaki Invariants and convex geometry on toric fano varieties. Osaka J Math, 1987, 24: 705-737
[31] Sakane Y.Examples of compact Kähler-Einstein manifolds with positive Ricci curvatures. Osaka J Math, 1986, 23: 585-617