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Takashi Sakai 
2010-03-21 
16:30 - 17:30 
308 , Mathematics Research Center Building (ori. New Math. Bldg.)

In 1991 Y.-G. Oh introduced the notion of tightness for Lagrangian submanifolds in Hermitian symmetric spaces. And he proved that the totally geodesic real projective space $\mathbb{R}P^n$ is the only tight Lagrangian submanifold in the complex projective space $\mathbb{C}P^n$ if $n \geq 2$. In this talk, first we give the classification of tight Lagrangian submanifold in $S^2 \times S^2$. We also show the global tightness of real forms of flag manifolds. Recently, Tanaka and Tasaki investigated the intersection of two real forms in Hermitian symmetric spaces of compact type. And they proved the global tightness of real forms.