Yang-Mills connections over a complex surface and harmonic curvature

Mitsuhiro Itoh

Compositio Mathematica (1987)

  • Volume: 62, Issue: 2, page 95-106
  • ISSN: 0010-437X

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Itoh, Mitsuhiro. "Yang-Mills connections over a complex surface and harmonic curvature." Compositio Mathematica 62.2 (1987): 95-106. <http://eudml.org/doc/89840>.

@article{Itoh1987,
author = {Itoh, Mitsuhiro},
journal = {Compositio Mathematica},
keywords = {anti-self dual connection; Yang-Mills equations; harmonic connection; positive scalar curvature; Yang-Mills connection},
language = {eng},
number = {2},
pages = {95-106},
publisher = {Martinus Nijhoff Publishers},
title = {Yang-Mills connections over a complex surface and harmonic curvature},
url = {http://eudml.org/doc/89840},
volume = {62},
year = {1987},
}

TY - JOUR
AU - Itoh, Mitsuhiro
TI - Yang-Mills connections over a complex surface and harmonic curvature
JO - Compositio Mathematica
PY - 1987
PB - Martinus Nijhoff Publishers
VL - 62
IS - 2
SP - 95
EP - 106
LA - eng
KW - anti-self dual connection; Yang-Mills equations; harmonic connection; positive scalar curvature; Yang-Mills connection
UR - http://eudml.org/doc/89840
ER -

References

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  1. 1 N. Aronszajn: A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order. J. Math. Pure et Appl.35 (1957) 235-249. Zbl0084.30402MR92067
  2. 2 M.F. Atiyah, N.J. Hitchin and I.M. Singer: Self-duality in four dimensional Riemannian geometry. Proc. Roy. Soc. London, Ser. A362 (1978) 425-461. Zbl0389.53011MR506229
  3. 3 J.P. Bourguignon and H.B. Lawson: Stability and isolation phenomena for Yang-Mills fields. Commun. Math. Phys.79 (1981) 189-230. Zbl0475.53060MR612248
  4. 4 S.K. Donaldson: An application of gauge theory to four dimensional topology. J. Differential Geometry18 (1983) 279-315. Zbl0507.57010MR710056
  5. 5 S.K. Donaldson: Anti self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles, Proc. London Math. Soc. (3) 50 (1985) 1-26. Zbl0529.53018MR765366
  6. 6 D.S. Freed and K. Uhlenbeck: Instantons and four-manifolds. New York: Springer-Verlag (1984). Zbl0559.57001MR757358
  7. 7 M. Itoh: On the moduli space of anti-self-dual Yang-Mills connections on Kähler surfaces. Pub. R.I.M.S. Kyoto19 (1983) 15-32. Zbl0536.53065MR700938
  8. 8 M. Itoh: The moduli space of Yang-Mills connections over a Kähler surface is a complex manifold. Osaka J. Math.22 (1985) 845-862. Zbl0567.53048MR815453
  9. 9 S. Kobayashi: Curvature and stability of vector bundles. Proc. Japan Acad. Ser. A, Math. Sci.58 (1982) 158-162. Zbl0538.32021MR664562
  10. 10 S. Kobayashi, Y. Ohnita and M. Takeuchi: On instability of Yang-Mills connections. Math. Z.193 (1986) 165-189. Zbl0634.53022MR856147
  11. 11 K. Kodaira and J. Morrow: Complex manifolds. Holt, Rinehalt and Winston (1971). Zbl0325.32001MR302937
  12. 12 Min-Oo: An L2-isolation theorem for Yang-Mills fields. Comp. Math.47 (1982) 153-163. Zbl0519.53042MR677017
  13. 13 C. Shen: The gap phenomena of Yang-Mills fields over the complete manifold. Math. Zeit.189 (1982) 69-77. Zbl0471.58031MR656222
  14. 14 C. Taubes: Stability in Yang-Mills theories. Commun. Math. Phys.91 (1983) 235-263. Zbl0524.58020MR723549

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