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| THE MODULI SPACE OF COMPLEX LAGRANGIAN SUBMANIFOLDSIN THE HYPER-KAEHLER MANIFOLD |
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Citation： |
FU Jixiang.THE MODULI SPACE OF COMPLEX LAGRANGIAN SUBMANIFOLDSIN THE HYPER-KAEHLER MANIFOLD[J].Chinese Annals of Mathematics B,1999,20(4):393~400 |
| Page view： 1179
Net amount： 922 |
Authors： |
FU Jixiang; |
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| Abstract： |
The deformation of a compact complex Lagrangian
submanifold in a hyper-Kaehler manifold and
the moduli space are studied. It is proved that the moduli space
$M_{\text{cl}}$ is a special Kaehler
manifold, where { special} means that there is a real flat torsionfree
symplectic connection $\nabla$ satisfying $d_{\nabla}\tilde{I}=0$ ($\tilde{I}$
is a complex structure of $M_{\text{cl}}$).
Thus, following [4], one knows that $T^{*}M_{\text{cl}}$ is a hyper-Kaehler
manifold and then that $M_{\text{cl}}$ is a complex Lagrangian submanifold in
$T^{*}M_{\text{cl}}$. |
Keywords： |
Moduli space, Complex Lagrangian submanifold,
Hyper-Kaehler manifold,Special Lagrangian submanifold,
Special Kaehler manifold, Deformation |
Classification： |
53C55 |
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