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Rotationally symmetric extremal pseudo-Kähler metrics of non-constant scalar curvatures

  • Xiaojuan Duan
Article
  • 43 Downloads

Abstract

In this paper, we explicitly construct some rotationally symmetric extremal (pseudo-)Kähler metrics of non-constant scalar curvature, which depend on some parameters, and on some line bundles over projective spaces. We also discuss the phase change phenomenon caused by the variation of parameters.

Keywords

Extremal pseudo-Kahler metric phase change rotationally symmetric 

Mathematics Subject Classification

53C56 58B20 

Notes

Acknowledgements

The author is partially supported by the Natural Science Foundation of Fujian Province (2013J01027) and is very grateful to Wei Li for his help in the revision process.

References

  1. 1.
    Abreu M, Toric Kähler metrics: cohomogenieity one examples of constant scalar cuvature in action-angle coordinates, Int. J. Math. 9 (1998) 641–651MathSciNetCrossRefGoogle Scholar
  2. 2.
    Apostolov V and Tønnesen-Friedman C, A remark on kähler metrics of constant scalar curvature on ruled complex surfaces, Bull. Lond. Math. Soc. 38 (2006) 494–500CrossRefzbMATHGoogle Scholar
  3. 3.
    Calabi E, Extremal Kähler metrics, in: Seminars on Differential Geometry, edited by S T Yau (1982) (Univ. of Tokyo Press, Tokyo) pp. 259–290Google Scholar
  4. 4.
    Candelas P and de La Ossa XC, Comments on conifold, Nucl. Phys. B 342 (1990) 246–248MathSciNetCrossRefGoogle Scholar
  5. 5.
    Duan X J and Zhou J, Rotationally symmetric pseudo-Kähler metrics of constant scalar curvatures, Sci. China Math. 54(5) (2011) 925-938MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Duan X J and Zhou J, Rotationally symmetric pseudo-Kähler–Einstein metrics, Front. Math. China 6(3) (2011) 391—410MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Simanca S R, A note on extremal metrics of non-constant scalar curvature, Isr. J. Math.78 (1992) 85–93MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Tønnesen-Friedman C, Extremal Kähler metrics on minimal ruled surfaces, J. Reine Angew. Math. 502 (1998) 175–197MathSciNetzbMATHGoogle Scholar
  9. 9.
    Tønnesen-Friedman C, Extremal Kähler metrics and hamiltonian functions I, J. Geom. Phys. 31 (1999) 25–34MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Tønnesen-Friedman C, Extremal Kähler metrics and hamiltonian functions II, Glasgow Math. J. 44 (2002) 241–253MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Indian Academy of Sciences 2018

Authors and Affiliations

  1. 1.Department of Applied MathematicsXiamen University of TechnologyXiamenChina

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