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Instantons and branes in manifolds with vector cross products

Conan Leung Chinese Univ of HK Jae-Hyouk Lee Washington University

Differential Geometry mathscidoc:1608.10089

Asian Journal of Mathematics, 12, (1), 121-144, 2008
In this paper we study the geometry of manifolds with vector cross products and its complexification. First we develop the theory of instantons and branes and study their deformations. For example they are (i) holomorphic curves and Lagrangian submanifolds in symplectic manifolds and (ii) associative submanifolds and coassociative submanifolds in G2-manifolds. Second we classify K¨ahler manifolds with the complex analog of the vector cross product, namely they are Calabi-Yau manifolds and hyperk¨ahler manifolds. Furthermore we study instantons, Neumann branes and Dirichlet branes on these manifolds. For example they are special Lagrangian submanifolds with phase angle zero, complex hypersurfaces and special Lagrangian submanifolds with phase angle pi/2 in Calabi-Yau manifolds.
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[ Download ] [ 2016-08-31 10:31:34 uploaded by conan ] [ 711 downloads ] [ 0 comments ] [ Cited by 9 ] 
@inproceedings{conan2008instantons,
  title={Instantons and branes in manifolds with vector cross products},
  author={Conan Leung, and Jae-Hyouk Lee},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160831103134787541565},
  booktitle={Asian Journal of Mathematics},
  volume={12},
  number={1},
  pages={121-144},
  year={2008},
}
Conan Leung, and Jae-Hyouk Lee. Instantons and branes in manifolds with vector cross products. 2008. Vol. 12. In Asian Journal of Mathematics. pp.121-144. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160831103134787541565.
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