Studies of compact homogeneous complex manifolds via of non-Kahler structures

• Project/Area Number: 22740040
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Geometry
• Research Institution: Shimane University
• Principal Investigator: YAMADA Takumi 島根大学, 総合理工学研究科, 准教授 (40403117)
• Project Period (FY): 2010 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000); Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 擬ケーラー多様体 / リー群 / リー環 / 等質空間 / リ―群 / 可解多様体 / 旗多様体 / 微分幾何学 / 等質複素多様体 / 非ケーラー構造 / 等質複素空間 / シンプレクティック幾何学

Research Abstract

I studies compact homogenous manifolds by using non-Kahler structures. I have constructed new examples of compact complex solvmanifolds which admit pseudo-Kahler structures, and I have shown that the Ricci curvatures of the above manifolds are zero. I also had that a Killing vector field on a compact pseudo-Kahler manifold is an infinitesimal automorphism of the complex structure. I also got results about signatures of pseudo-Kahler metrics on flag manifolds.

Research Products

• [Journal Article] Ricci flatness of certain compact pseudo-Kahler solvmanifolds (2012)
  • Author(s): 山田拓身
  • Journal Title: Journal of Geometry and Physics Volume: 62巻 Pages: 1338-1345
  • URL: http://dx.doi.org/10.1016/j.geomphys.2011.06.006
  • Peer Reviewed
• [Journal Article] Holomorphic vector fields of compact pseudo- Kahler manifolds (2012)
  • Author(s): 山田拓身
  • Journal Title: Journal of Geometry and Physics Volume: 62巻 Pages: 740-745
  • URL: http://dx.doi.org/10.1016/j.geomphys.2011.08.001
  • Peer Reviewed
• [Journal Article] Ricci flatness of certain compact pseudo-Kahlersolvmanifolds (2012)
  • Author(s): 山田拓身
  • Journal Title: Journal of Geometry and Physics Volume: Vol.62 Issue: 5 Pages: 1338-1345
  • DOI: 10.1016/j.geomphys.2011.06.006
  • Peer Reviewed
• [Journal Article] Ricci flatness of certain compact pseudo-Kahler solvmanifolds (2011)
  • Author(s): T.Yamada
  • Journal Title: Journal of Geometry and Physics Volume: Vol.62 Issue: 4 Pages: 1-8
  • DOI: 10.1016/j.geomphys.2011.08.001
  • Peer Reviewed
• [Presentation] 一般化された旗多様体の不変擬ケーラー構造の指数について (2013)
  • Author(s): 山田拓身
  • Organizer: 多様体と幾何構造の融合
  • Place of Presentation: 多様体と幾何構造の融合
  • Year and Date: 2013-03-06
• [Presentation] 一般化された旗多様体の不変擬ケーラー構造の指数について (2013)
  • Author(s): 山田拓身
  • Organizer: 多様体と幾何構造の融合
  • Place of Presentation: 名城大学(名古屋市)
  • Invited
• [Presentation] 非ケーラー構造をもつ複素等質空間の正則ベクトル場について (2012)
  • Author(s): 山田拓身
  • Organizer: 複素解析的ベクトル場・葉層構造とその周辺
  • Place of Presentation: 龍谷大学セミナーハウスともいき荘(京都)
  • Year and Date: 2012-12-07
• [Presentation] 非ケーラー構造をもつ複素等質空間の正則ベクトル場について (2012)
  • Author(s): 山田拓身
  • Organizer: 複素解析的ベクトル場・葉層構造とその周辺
  • Place of Presentation: 龍谷大学セミナーハウスともいき荘(京都市)
  • Invited
• [Presentation] Some studies on compact non-Kaehler manifolds (2011)
  • Author(s): 山田拓身
  • Organizer: 松江微分幾何学研究会 2011
  • Place of Presentation: 島根大学(松江)
  • Year and Date: 2011-12-17
• [Presentation] コンパクト擬ケーラー多様体の正則ベクトル場について (2010)
  • Author(s): 山田拓身
  • Organizer: 擬リーマン幾何学の展開 III
  • Place of Presentation: お茶の水大学(東京)
  • Year and Date: 2010-12-19
• [Presentation] コンパクト擬ケーラー多様体の正則ベクトル場について (2010)
  • Author(s): 山田拓身
  • Organizer: 擬リーマン幾何学の展開III
  • Place of Presentation: お茶の水女子大学(招待講演)
  • Year and Date: 2010-12-19
• [Presentation] コンパクト擬ケーラー多様体の正則ベクトル場について (2010)
  • Author(s): 山田拓身
  • Organizer: 松江微分幾何学研究会 2010
  • Place of Presentation: 島根大学 (松江)
  • Year and Date: 2010-12-11
• [Remarks]
  • URL: http://www.shimane-u.ac.jp/docs/2010113000376/files/treasure5.pdf
• [Remarks]
  • URL: http://www.shimane-u.ac.jp/docs/2010113000376/files/treasure5.pdf