Submanifold Theory and Study of Circles

子流形理论与圆的研究

• 批准号: 14540080
• 负责人: MAEDA Sadahiro
• 金额: $ 1.54万
• 依托单位: Shimane University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540080/
• 关键词: symmetric spaces; geodesic spheres; constant isotropic submanifolds; Killing ordinary helices; complex space forms; Veronese embeddings; extrinsic spheres; 測地線; 円; 常螺旋; 実超曲面; nuled実超曲面; ケーラー部分多様体; Veronese埋蔵; 複素射影空間; ruled実超曲面

(1) We study length spectrum of geodesic spheres in rank one symmetric spaces.(2) We characterize constant isotropic immersions by circles.(3) We investigate bondedness and unboundedness of Killing ordinary helices on a complex hyperbolic plane, respectively.(4) We show that every real hypersurface of a nonflat complex space form is irreducible.(5) We characterize extrinsic spheres in a Riemannian manifold by circles.(6) We characterize Veronese embeddings of complex projective spaces into complex projective spaces by circles.

(1)研究了秩一对称空间中测地球的长度谱。(2)我们用圆刻画了常数各向同性浸入。(3)研究了复双曲平面上Killing螺旋线的有键性和无界性。(4)证明了非平坦复空间形式的每个真实的超曲面都是不可约的。(5)我们用圆刻画了黎曼流形中的外球面。(6)利用圆刻画了复射影空间到复射影空间的Veronese嵌入。

项目成果

T.Adachi, S.Maeda: "Characterization of complex space forms"Nihonkai Math.J.. 14. 95-98 (2003)

T.Adachi、S.Maeda：“复杂空间形式的表征”Nihonkai Math.J.. 14. 95-98 (2003)

T.Adachi, S.Maeda: "Geometry of ordinary helices"Hokkaido Math.J. 33. 233-246 (2004)

T.Adachi、S.Maeda：“普通螺旋的几何”Hokkaido Math.J。

足立俊明, 前田定廣: "Holomorphic helix of proper order 3 on a complex hyperbolic plane"Topology and its Applications. (受理済).

Toshiaki Adachi、Sadahiro Maeda：“复杂双曲平面上的真阶 3 的全纯螺旋”拓扑及其应用（已接受）。

S.Maeda: "A characterization of isotropic immersions"Archiv der Mathematik. 81. 90-95 (2003)

S.Maeda：“各向同性沉浸的表征”Archiv der Mathematik。

前田定廣: "A characterization of constant isotropic immersions by circles"Archiv der Math.. (受理済).

Sadahiro Maeda：“圆对恒定各向同性浸入的表征”Archiv der Math..（已接受）。