Yang-Mills bar connections over compact Kähler manifolds
Archivum Mathematicum (2010)
- Volume: 046, Issue: 1, page 47-69
- ISSN: 0044-8753
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topVân 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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- Kobayashi, S., Differential geometry of complex vector bundles, Iwanami Shoten Publishers and Princeton University Press, 1987. (1987) Zbl0708.53002MR0909698
- Koszul, J. L., Malgrange, B., 10.1007/BF02287068, Arch. Math. (Basel) 9 (1958), 102–109. (1958) MR0131882DOI10.1007/BF02287068
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