Yang-Mills bar connections over compact Kähler manifolds

Hông Vân Lê

Archivum Mathematicum (2010)

  • Volume: 046, Issue: 1, page 47-69
  • ISSN: 0044-8753

Abstract

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In this note we introduce a Yang-Mills bar equation on complex vector bundles E provided with a Hermitian metric over compact Hermitian manifolds. According to the Koszul-Malgrange criterion any holomorphic structure on E can be seen as a solution to this equation. We show the existence of a non-trivial solution to this equation over compact Kähler manifolds as well as a short time existence of a related negative Yang-Mills bar gradient flow. We also show a rigidity of holomorphic connections among a class of Yang-Mills bar connections over compact Käahler manifolds of positive Ricci curvature.

How to cite

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Vân Lê, Hông. "Yang-Mills bar connections over compact Kähler manifolds." Archivum Mathematicum 046.1 (2010): 47-69. <http://eudml.org/doc/37653>.

@article{VânLê2010,
abstract = {In this note we introduce a Yang-Mills bar equation on complex vector bundles $E$ provided with a Hermitian metric over compact Hermitian manifolds. According to the Koszul-Malgrange criterion any holomorphic structure on $E$ can be seen as a solution to this equation. We show the existence of a non-trivial solution to this equation over compact Kähler manifolds as well as a short time existence of a related negative Yang-Mills bar gradient flow. We also show a rigidity of holomorphic connections among a class of Yang-Mills bar connections over compact Käahler manifolds of positive Ricci curvature.},
author = {Vân Lê, Hông},
journal = {Archivum Mathematicum},
keywords = {Kähler manifold; complex vector bundle; holomorphic connection; Yang-Mills bar gradient flow; Kähler manifold; complex vector bundle; holomorphic connection; Yang-Mills bar gradient flow},
language = {eng},
number = {1},
pages = {47-69},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Yang-Mills bar connections over compact Kähler manifolds},
url = {http://eudml.org/doc/37653},
volume = {046},
year = {2010},
}

TY - JOUR
AU - Vân Lê, Hông
TI - Yang-Mills bar connections over compact Kähler manifolds
JO - Archivum Mathematicum
PY - 2010
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 046
IS - 1
SP - 47
EP - 69
AB - In this note we introduce a Yang-Mills bar equation on complex vector bundles $E$ provided with a Hermitian metric over compact Hermitian manifolds. According to the Koszul-Malgrange criterion any holomorphic structure on $E$ can be seen as a solution to this equation. We show the existence of a non-trivial solution to this equation over compact Kähler manifolds as well as a short time existence of a related negative Yang-Mills bar gradient flow. We also show a rigidity of holomorphic connections among a class of Yang-Mills bar connections over compact Käahler manifolds of positive Ricci curvature.
LA - eng
KW - Kähler manifold; complex vector bundle; holomorphic connection; Yang-Mills bar gradient flow; Kähler manifold; complex vector bundle; holomorphic connection; Yang-Mills bar gradient flow
UR - http://eudml.org/doc/37653
ER -

References

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  2. Donaldson, S. K., Kronheimer, P. B., The geometry of 4-manifolds, Clarendon Press, Oxford, 1990. (1990) MR1079726
  3. Griffiths, P., Harris, J., Principles of algebraic geometry, 2nd ed., Wiley Classics Library, New York, 1994. (1994) Zbl0836.14001MR1288523
  4. Hamilton, R., Three manifold with positive Ricci curvature, J. Differential Geom. 17 (2) (1982), 255–306. (1982) MR0664497
  5. Kobayashi, S., Differential geometry of complex vector bundles, Iwanami Shoten Publishers and Princeton University Press, 1987. (1987) Zbl0708.53002MR0909698
  6. Koszul, J. L., Malgrange, B., 10.1007/BF02287068, Arch. Math. (Basel) 9 (1958), 102–109. (1958) MR0131882DOI10.1007/BF02287068

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