Submanifolds and homogeneous curves

2014 Fiscal Year Final Research Report

• Project/Area Number: 23540097
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Saga University
• Principal Investigator: MAEDA Sadahiro 佐賀大学, 工学(系)研究科(研究院), 教授 (40181581)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: 微分幾何学 / 実超曲面論 / 等質実超曲面 / 線織実超曲面 / 測地線 / 円 / 接触形式 / 外微分

Outline of Final Research Achievements

There are almost results related to real hypersurfaces in a nonflat complex space form which is either a complex projective space or a complex hyperbolic space. It is known that there does not exist a real hypersurface all of whose geodesics are mapped to circles in a nonflat complex space form. From this viewpoint we consider three real hypersurfaces in this ambient space. This result is a main theorem in this study. Another main theorem is a classification theorem of minimal ruled real hypersurfaces in a nonflat complex space form. Complex projective space admits just one minimal ruled real hypersurface. However Complex hyperbolic space admits three minimal ruled real hypersurfaces. This result depends on the sign of sectional curvatures of these ambient spaces. From this viewpoint this result is interesting.

Free Research Field

数学（幾何学）