Self-duality of Kähler surfaces

Mitsuhiro Itoh

Compositio Mathematica (1984)

  • Volume: 51, Issue: 2, page 265-273
  • ISSN: 0010-437X

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Itoh, Mitsuhiro. "Self-duality of Kähler surfaces." Compositio Mathematica 51.2 (1984): 265-273. <http://eudml.org/doc/89645>.

@article{Itoh1984,
author = {Itoh, Mitsuhiro},
journal = {Compositio Mathematica},
keywords = {Penrose twistor space construction; Kähler metric; Kähler surface; anti-self-dual; scalar curvature},
language = {eng},
number = {2},
pages = {265-273},
publisher = {Martinus Nijhoff Publishers},
title = {Self-duality of Kähler surfaces},
url = {http://eudml.org/doc/89645},
volume = {51},
year = {1984},
}

TY - JOUR
AU - Itoh, Mitsuhiro
TI - Self-duality of Kähler surfaces
JO - Compositio Mathematica
PY - 1984
PB - Martinus Nijhoff Publishers
VL - 51
IS - 2
SP - 265
EP - 273
LA - eng
KW - Penrose twistor space construction; Kähler metric; Kähler surface; anti-self-dual; scalar curvature
UR - http://eudml.org/doc/89645
ER -

References

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  1. [1] M.F. Atiyah, N.J. Hitchin and I.M. Singer: Self-duality in four-dimensional Riemannian geometry. Proc. R. Soc. Lond. A.362 (1978) 425-461. Zbl0389.53011MR506229
  2. [2] J.P. Bourguignon: Les variétés de dimension 4 à signature non nulle dont la courbure est harmonique sont d'Einstein. Invent. Math.63 (1981) 263-286. Zbl0456.53033MR610539
  3. [3] B.-Y. Chen: Some topological obstructions to Bochner-Kaehler metrics and their applications. Jour. Dif. Geom.13 (1978) 547-558. Zbl0354.53049MR570217
  4. [4] A. Derdzinski: Exemples de métriques de Kähler et d'Einstein auto-duales sur le plan complexe. In: Geometrie riemannienne en dimension 4. Seminaire Arthur Besse 1978/79, Cedic/Fernand Nathan, Paris (1981). Zbl0477.53025
  5. [5] A. Derdzinski: Self-dual Kähler manifolds and Einstein manifolds of dimension four. Comp. Math.49 (405-433) 1983. Zbl0527.53030MR707181
  6. [6] L.P. Eisenhart: Riemannian Geometry. Princeton (1964). Zbl0041.29403JFM52.0721.01
  7. [7] S. Helgason: Differential Geometry, Lie Groups, and Symmetric Spaces. Academic Press (1978). Zbl0451.53038MR514561
  8. [8] N.J. Hitchin: Kählerian twistor spaces. Proc. Lond. Math. Soc.43 (1981) 133-150. Zbl0474.14024MR623721
  9. [9] M. Itoh: On the moduli space of anti-self-dual Yang-Mills connections on Kähler surfaces. Publ. Res. Inst. Math. Sci.19 (1983) 15-32. Zbl0536.53065MR700938
  10. [10] S. Kobayashi and K. Nomizu: Foundations of differential geometry, II. Interscience Publishers (1969). Zbl0175.48504
  11. [11] K. Kodaira: On the structure of complex analysic surfaces, IV. Amer. J. Math.90 (1968) 1048-1066. Zbl0193.37702MR239114
  12. [12] K. Kodaira and J. Morrow: Complex Manifolds. Holt, Rinehart and Winston (1971). Zbl0325.32001MR302937
  13. [13] F. Tricerri and L. Vanhecke: Curvature tensors on almost Hermitian manifolds. Transact. A.M.S.267 (1981) 365-398. Zbl0484.53014MR626479
  14. [14] K. Yano and S. Bochner: Curvature and Betti numbers. Ann. Math. Studies32, Princeton (1953). Zbl0051.39402MR62505
  15. [15] S.-T. Yau: On the curvature of compact Hermitian manifolds. Invent. Math.25 (1974) 213-239. Zbl0299.53039MR382706
  16. [16] S.-T. Yau: Seminar on differential geometry. Ann. Math. Studies102, Princeton (1982). Zbl0479.53001MR645728

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