茨城大学
理学部
理学科(数学・情報数理コース)

准教授

入江 博

イリエ ヒロシ
IRIE HIROSHI

論文

  1. 研究論文(学術雑誌) 共著 Almost all Lagrangian torus orbits in CP^n are not Hamiltonian volume minimizing Iriyeh, Hiroshi; Ono, Hajime Ann. Global Anal. Geom. Springer 50/ 1, 85-96 2016/07
  2. 研究論文(国際会議プロシーディングス) 共著 Lagrangian intersection theory and Hamiltonian volume minimizing problem Iriyeh, Hiroshi; Sakai, Takashi; Tasaki, Hiroyuki Springer Proc. Math. Stat. Springer, Tokyo 106, 391-399 2014 In this article, we first describe antipodal sets and the structure of intersections of two real forms in complex flag manifolds. In particular, in the complex flag manifold consisting of sequences of complex subspaces in a complex vector space we investigate the real form consisting of sequences of quaternionic subspaces. Moreover, we discuss applications to the Hamiltonian volume minimizing problem.
  3. Lagrangian Floer homology of a pair of real forms in Hermitian symmetric spaces of compact type IRIYEH Hiroshi, SAKAI Takashi, TASAKI Hiroyuki Journal of the Mathematical Society of Japan The Mathematical Society of Japan 65/ 4, 1135-1151 2013 0025-5645 URL In this paper we calculate the Lagrangian Floer homology HF(L0,L1:Z2) of a pair of real forms (L0,L1) in a monotone Hermitian symmetric space M of compact type in the case where L0 is not necessarily congruent to L1. In particular, we have a generalization of the Arnold-Givental inequality in the case where M is irreducible. As its application, we prove that the totally geodesic Lagrangian sphere in the complex hyperquadric is globally volume minimizing under Hamiltonian deformations.
  4. Integral geometry and Hamiltonian volume minimizing property of a totally geodesic Lagrangian torus in S2×S2 Iriyeh Hiroshi, Ono Hajime, Sakai Takashi Proceedings of the Japan Academy Ser. A Mathematical Sciences Japan Academy 79/ 10, 167-170 2003/12 03862194 URL

研究発表

  1. 口頭発表(一般) 等径超曲面のGauss像のHamiltonian non-displaceabilityについて 日本数学会2016年度年会 2016/03/16 等径超曲面のGauss像は複素2次超曲面というHermite対称空間のLagrange部分多様体になるが、それらがいくつかの例を除いてHamiltonian non-displaceabilityであることを示した共同研究の成果について報告した。
  2. 公開講演,セミナー,チュートリアル,講習,講義等 Almost all Lagrangian torus orbits in the complex projective space are not Hamiltonian volume minimizing Joint NCTS Differential Geometry and NCKU-RCTS symplectic geometry seminar 2015/09/25 複素射影空間のLagrangeトーラス軌道のほとんどが、Hamilton安定であるにもかかわらず、Hamilton体積最小ではないことを証明した小野肇氏(埼玉大学)との共同研究の成果について講演した。