• 한국수학교육학회지시리즈B:순수및응용수학
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• 제22권1호
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• pp.13-23
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• 2015

We introduce a decomposition on a symplectic subspace determined by symplectic structure and study its properties. As a consequence, we give an elementary proof of the deformation of the Grassmannians of symplectic subspaces to the complex Grassmannians.

• 대한수학회지
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• 제52권5호
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• pp.1109-1122
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• 2015

A Schubert variety in a rational homogeneous variety G/P is defined by the closure of an orbit of a Borel subgroup B of G. In general, Schubert varieties are singular, and it is an old problem to determine which Schubert varieties are smooth. In this paper, we classify all smooth Schubert varieties in the symplectic Grassmannians.

• 대한수학회지
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• 제53권3호
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• pp.489-501
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• 2016

In this paper, we study the rigidity under $K{\ddot{a}}hler$ deformation of the complex structure of odd Lagrangian Grassmannians, i.e., the Lagrangian case $Gr_{\omega}$(n, 2n+1) of odd symplectic Grassmannians. To obtain the global deformation rigidity of the odd Lagrangian Grassmannian, we use results about the automorphism group of this manifold, the Lie algebra of infinitesimal automorphisms of the affine cone of the variety of minimal rational tangents and its prolongations.