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KAKEN_16K17598seika.pdf
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微分幾何学的手法によるカラビ・ヤウ多様体と特殊ラグランジュ部分多様体の研究
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ビブン キカガクテキ シュホウ ニ ヨル カラビ・ヤウ タヨウタイ ト トクシュ ラグランジュ ブブン タヨウタイ ノ ケンキュウ
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Bibun kikagakuteki shuhō ni yoru Karabi Yau tayōtai to tokushu Raguranju bubun tayōtai no kenkyū
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On the Calabi-Yau manifolds and the special Lagrangian submanifolds from the view point of differential geometry
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服部, 広大
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ハットリ, コウタ
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Hattori, Kōta
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慶應義塾大学・理工学部 (矢上) ・准教授
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Research team head
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科研費研究者番号 : 30586087
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2020
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科学研究費補助金研究成果報告書
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2019
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微分幾何学の文脈において、自明な標準束をもつリッチ平坦ケーラー計量をもつ複素多様体をカラビ・ヤウ多様体という。さらに強く、正則シンプレクティック形式をもつ場合は超ケーラー多様体と呼ばれる。
完備リッチ平坦多様体がユークリッド的な体積の増大度を持ち、無限遠点における接錐の一つが滑らかな切断を持つならば、無限遠点における接錐がただ一つしかないことがコーディングとミニコッチによって証明されている。これに対して研究代表者は、無限遠点における接錐のモジュライ空間が円周と同相になるような超ケーラー多様体を発見した。
In the context of differential geometry, Calabi-Yau manifolds are Ricci-flat Kaehler manifolds with trivial canonical bundle. Moreover, if the manifolds have holomorphic symplectic form, then they are called the hyper-Kaehler manifolds.
It is shown by Colding and Minicozzi that if a complete Ricci-flat manifold with maximal volume growth and one of the tangent cone at infinity has a smooth cross section, then the tangent cone at infinity is unique. We investigate the asymptotic behavior of one of the hyper-Kaehler manifolds constructed by Anderson-Kronheimer-LeBrun, which is known to have the irrational volume growth, then show that the moduli space of the tangent cones at infinity of it is homeomorphic to the circle.
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研究種目 : 若手研究 (B)
研究期間 : 2016～2019
課題番号 : 16K17598
研究分野 : 微分幾何学
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