| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2019: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Outline of Final Research Achievements |
A generalization of theorem of Tsunero Takahashi and do Carmo-Wallach theory leads us to the concept of the terminal harmonic map into Grassmann manifolds. When the gauge condition is fixed, the terminal harmonic map is defined as the harmonic map satisfying the given gauge condition into Grassmannian of the lowest dimension. It has the rigidity and any harmonic map except the terminal one admits deformations.
The moduli space of holomorphic isometric immersion of algebraic manifolds into a complex quadric modulo gauge equivalence is a complex submanifold of a complex Euclidean space, which has a Kaehler structure with a circle action. Then the moduli space of those maps modulo image equivalence is the quotient of the moduli modulo gauge equivalence by the circle action.
Applying the theory, we obtain the explicit description of the moduli spaces of holomorphic isometric embeddings from the complex projective space and the complex Grassmannian of two-planes into complex quadrics.
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