Research of transverse geometric structures on foliated manifolds

• Project/Area Number: 21740051
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Geometry
• Research Institution: Kyoto University
• Principal Investigator: MORIYAMA Takayuki 京都大学, 理学研究科, 助教 (60532554)
• Project Period (FY): 2009 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000); Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: 微分幾何学 / 葉層構造 / カラビ・ヤウ構造 / 変形理論 / 佐々木多様体 / 横断的ケーラー構造 / ルジャンドル部分多様体 / 横断的カラビ・ヤウ構造 / モジュライ空間 / 佐々木・アインシュタイン構造

Research Abstract

(1) We show that there exists a smooth metric on the set of transverse Riemannian metrics on foliated manifolds with taut foliations
(2) We prove that the moduli space of transverse Calabi-Yau structures on foliated manifolds with taut foliations is Hausdorff and a smooth manifold, and compute the dimension of the moduli spaces in some examples.
(3) We provide a deformation theory of special Legendrian submanifolds in Sasaki-Einstein manifolds.

Research Products

• [Journal Article] The moduli space of transverse Calabi-Yau structures on foliated manifolds (2011)
  • Author(s): Takayuki Moriyama
  • Journal Title: Osaka Journal of Mathematics Volume: 48巻 Pages: 383-413
  • NAID: 120005986566
  • Peer Reviewed
• [Journal Article] Deformations of transverse Calabi-Yau structures on foliated manifolds (2010)
  • Author(s): Takayuki Moriyama
  • Journal Title: Publications of the RIMS. Kyoto univ Volume: 46巻(2) Pages: 335-357
  • Peer Reviewed
• [Journal Article] Deformations of transverse Calabi-Yau structures on foliated manifolds (2010)
  • Author(s): Takayuki Moriyama
  • Journal Title: Publications of the RIMS.Kyoto univ. Volume: 46巻(2) Pages: 335-357
  • Peer Reviewed
• [Presentation] 佐々木・アインシュタイン多様体における特殊ルジャンドル部分多様体の変形について (2013)
  • Author(s): 森山貴之
  • Organizer: 日本数学会幾何学分科会
  • Place of Presentation: 京都大学
  • Year and Date: 2013-03-21
• [Presentation] Special Legendrian submanifolds in toric Sasaki-Einstein manifolds (2012)
  • Author(s): Takayuki Moriyama
  • Organizer: UK-JAPAN MATHEMATICAL FORUM" on Geometry, Probability, and their Applications
  • Place of Presentation: 慶応大学
  • Year and Date: 2012-07-17
• [Presentation] トーリック佐々木・アインシュタイン多様体における特殊ルジャンドル部分多様体 (2012)
  • Author(s): 森山貴之
  • Organizer: 日本数学会幾何学分科会
  • Place of Presentation: 東京理科大学
  • Year and Date: 2012-03-27
• [Presentation] トーリック佐々木・アインシュタイン多様体における特殊ルジャンドル部分多様体 (2012)
  • Author(s): 森山貴之
  • Organizer: 日本数学会幾何学分科会
  • Place of Presentation: 東京理科大学(東京)
  • Year and Date: 2012-03-27
• [Presentation] Special Legendrian submanifolds in toric Sasaki-Einstein manifolds (2012)
  • Author(s): Takayuki Moriyama
  • Organizer: ``UK-JAPAN MATHEMATICAL FORUM'' on Geometry, Probability, and their Applications
  • Place of Presentation: 慶応大学
  • Invited
• [Presentation] Special Legendrian submanifolds in toric Sasaki-Einstein manifolds (partI&II) (2012)
  • Author(s): 森山貴之
  • Organizer: 第6回GEOSOCKセミナー「幾何学と数理物理」
  • Place of Presentation: 大阪市立大学(大阪府)(招待講演)
• [Presentation] Special Legendrian submanifolds in toric Sasaki-Einstein manifolds (2011)
  • Author(s): Takayuki Moriyama
  • Organizer: The 17th InternationalSymposium on ``Complex Geometry"
  • Place of Presentation: ホテルゾンタック(長野県)
  • Year and Date: 2011-11-10
• [Presentation] Special Legendrian submanifolds in toric Sasaki-Einstein manifolds (2011)
  • Author(s): Takayuki Moriyama
  • Organizer: The 17th International Symposium on Complex Geometry
  • Place of Presentation: ホテルゾンタック(長野県)
  • Year and Date: 2011-11-10
• [Presentation] 葉層多様体における横断的カラビ・ヤウ構造のモジュライ空間 (2010)
  • Author(s): 森山貴之
  • Organizer: 松江微分幾何学研究集会
  • Place of Presentation: 島根大学(島根県)
  • Year and Date: 2010-12-11
• [Presentation] 葉層多様体における横断的カラビ・ヤウ構造のモジュライ空間 (2010)
  • Author(s): 森山貴之
  • Organizer: トポロジー幾何学セミナー
  • Place of Presentation: 広島大学(広島県)
  • Year and Date: 2010-10-19
• [Presentation] 葉層多様体における横断的カラビ・ヤウ構造のモジュライ空間 (2010)
  • Author(s): 森山貴之
  • Organizer: 第57回幾何学シンポジウム
  • Place of Presentation: 神戸大学
  • Year and Date: 2010-08-07
• [Presentation] 葉層多様体における横断的カラビ・ヤウ構造のモジュライ空間 (2010)
  • Author(s): 森山貴之
  • Organizer: 第57回幾何学シンポジウム
  • Place of Presentation: 神戸大学(兵庫県)
  • Year and Date: 2010-08-07
• [Presentation] 葉層多様体における横断的カラビ・ヤウ構造のモジュライ空間 (2010)
  • Author(s): 森山貴之
  • Organizer: 日本数学会幾何学分科会
  • Place of Presentation: 慶応大学
  • Year and Date: 2010-03-26
• [Presentation] The moduli space of transverse Calabi-Yau structureson foliated Manifolds (2010)
  • Author(s): Takayuki Moriyama
  • Organizer: 第2回GCOE若手数学者交流会
  • Place of Presentation: 京都大学
  • Year and Date: 2010-02-22
• [Presentation] The moduli space of transverse Calabi-Yau structures on foliated Manifolds (2010)
  • Author(s): 森山貴之
  • Organizer: 第2回GCOE若手数学者交流会
  • Place of Presentation: 京都大学
  • Year and Date: 2010-02-22
• [Presentation] The moduli space of transverse Calabi-Yau structureson foliated Manifolds (2010)
  • Author(s): Takayuki Moriyama
  • Organizer: 国際カンファレンス``日中友好幾何学研究集会
  • Place of Presentation: OIST (沖縄科学技術研究基盤整備機構) Seaside House
  • Year and Date: 2010-01-30
• [Presentation] The moduli space of transverse Calabi-Yau structures on foliated Manifolds (2010)
  • Author(s): 森山貴之
  • Organizer: 国際カンファレンス"日中友好幾何学研究集会"
  • Place of Presentation: OIST(沖縄科学技術研究基盤整備機構)Seaside House
  • Year and Date: 2010-01-30
• [Presentation] Deformations of transverse Calabi-Yau structures on foliated manifolds (2009)
  • Author(s): Takayuki Moriyama
  • Organizer: 国際カンファレンス``Geometry and Quantization"
  • Place of Presentation: ルクセンブルク大学(ルクセンブルク)
  • Year and Date: 2009-09-10
• [Presentation] Deformations of transverse Calabi-Yau structures on foliated manifolds (2009)
  • Author(s): 森山貴之
  • Organizer: 国際カンファレンス"Geometry and Quantization"
  • Place of Presentation: ルクセンブルク大学(ルクセンブルク)
  • Year and Date: 2009-09-10
• [Presentation] 葉層多様体における横断的カラビ・ヤウ構造の変形 (2009)
  • Author(s): 森山貴之
  • Organizer: 名古屋大学幾何学セミナー
  • Place of Presentation: 名古屋大学
  • Year and Date: 2009-06-09