ON SOME ROTATIONALLY SYMMETRIC GRADIENT PSEUDO-KÄHLER-RICCI SOLITONS

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (1): 269-288.

ON SOME ROTATIONALLY SYMMETRIC GRADIENT PSEUDO-KÄHLER-RICCI SOLITONS

段孝娟

Department of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, China

收稿日期:2016-09-30 修回日期:2017-08-11 出版日期:2018-02-25 发布日期:2018-02-25
作者简介:Xiaojuan DUAN,E-mail:2010111012@xmut.edu.cn
基金资助:
The author is partially supported by the Natural Science Foundation of Fujian Province (2013J01027).

ON SOME ROTATIONALLY SYMMETRIC GRADIENT PSEUDO-KÄHLER-RICCI SOLITONS

Xiaojuan DUAN

Department of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, China

Received:2016-09-30 Revised:2017-08-11 Online:2018-02-25 Published:2018-02-25
Supported by:
The author is partially supported by the Natural Science Foundation of Fujian Province (2013J01027).

摘要/Abstract

摘要： In this paper, we explicitly construct some rotationally symmetric gradient pseudo-Kähler-Ricci solitons which depend on some parameters, on some line bundles and other bundles over projective spaces. We also discuss the "phase change" phenomenon caused by the variation of parameters.

关键词: pseudo-Kahler-Ricci soliton, rotationally symmetric, phase change, gradient soliton

Abstract: In this paper, we explicitly construct some rotationally symmetric gradient pseudo-Kähler-Ricci solitons which depend on some parameters, on some line bundles and other bundles over projective spaces. We also discuss the "phase change" phenomenon caused by the variation of parameters.

Key words: pseudo-Kahler-Ricci soliton, rotationally symmetric, phase change, gradient soliton

段孝娟. ON SOME ROTATIONALLY SYMMETRIC GRADIENT PSEUDO-KÄHLER-RICCI SOLITONS[J]. 数学物理学报(英文版), 2018, 38(1): 269-288.

Xiaojuan DUAN. ON SOME ROTATIONALLY SYMMETRIC GRADIENT PSEUDO-KÄHLER-RICCI SOLITONS[J]. Acta mathematica scientia,Series B, 2018, 38(1): 269-288.

参考文献

[1] Calabi E. Extremal Kähler metrics//Yau S T, Seminars on Differential Geometry. Tokyo:Princeton and Univ of Tokyo Press, 1982:259-290
[2] Candelas P, de La Ossa X C. Comments on conifold. Nucl Phys B, 1990, 342:246-248
[3] Cao H -D. Existence Of Gradient Kähler-Ricci Solitons//Chow B, Gulliver R, Levy S, Sullivan J. Elliptic and Parabolic Methods in Geometry, 1996:1-16
[4] Cao H -D. Limits of solutions to the Kähler-Ricci flow. J Differ Geom, 1997, 45(2):257-272
[5] Cao H -D. Geometry of Ricci solitons. Chin Ann Math, 2006, 27B(1):121-142
[6] Cao H -D, Zhou D T. On complete gradient shrinking Ricci solitons. J Differ Geom, 2009, 85(2):175-185
[7] Cao H -D. Recent progress on Ricci solitons. Advanced Lectures in Mathematics, 2010, 11:1-38
[8] Dancer A S, Wang M -Y. On Ricci solitons of cohomogeneity one. arXiv:08020759
[9] Duan X -J, Zhou J. Rotationally symmetric pseudo-Kähler-Einstein metrics. Front Math China, 2011, 6(3):391-410
[10] Duan X -J, Zhou J. Rotationally symmetric pseudo-Kähler metrics of constant scalar curvatures. Sci China Math, 2011, 54(5):925-938
[11] Feldman M, Ilmanen T, Knopf D. Rotationaly symmetric shringking and expanding gradient Kähle-Ricci solitons. J Differ Geom, 2003, 65:169-209
[12] Feitosa F E S, Freitas A A, Gomes J N V, Pina R S. On the construction of gradient Ricci soliton warped product. Nonlinear Anal TMA, 2017, 161:30-43
[13] Hamilton R. Three-manifolds with positive Ricci curvature. J Differ Geom, 1982, 17:255-306
[14] Hamilton R S. The formation of singularities in the Ricci flow//Combridge M A. J Differ Geom, 1995, 2:7-136
[15] Koiso N. On rotionally symmetric Hamilton's equation for Kähler-Einstein metrics//Recent Topics in Diff Anal Geom, Adv Studies in Pure Math, 18-I. Boston, MA:Academic Press, 1990:327-337
[16] Kotschwar B. On rotationally invariant shrinking gradient Ricci solitons. Pacific J Math, 2008, 236(1):70-85
[17] Li C. On rotationally symmetric Kähler-Ricci solitons. Mathematics, 2010, arXiv:10044049
[18] Petersen P, Wylie W. On the classifiation of gradient Ricci solitons. Geom Topol, 2008, 14(4):2277-2300
[19] Petersen P, Wylie W. On gradient Ricci solitons with symmetry. Proc Amer Math Soc, 2010, 137(2):2085-2092
[20] Su Y H, Zhang K. On the Kähler-Ricci solitons with vanishing Bochner-Weyl tensor. Acta Math Sci, 2012, 32B(3):1239-1244
[21] Yang B. A characterization of Koiso's typed solitons. Mathematics, 2008. arXiv:math.DG/0802.0300

ON SOME ROTATIONALLY SYMMETRIC GRADIENT PSEUDO-KÄHLER-RICCI SOLITONS

ON SOME ROTATIONALLY SYMMETRIC GRADIENT PSEUDO-KÄHLER-RICCI SOLITONS

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 0

Metrics

本文评价

推荐阅读 10