Classification of flat slant surfaces in complex Euclidean plane : In memory of Professor Seiichi Yamaguchi
スポンサーリンク
概要
- 論文の詳細を見る
It is well-known that the classification of flat surfaces in Euclidean 3-space is one of the most basic results in differential geometry. For surfaces in the complex Euclidean plane \bm{C}<SUP>2</SUP> endowed with almost complex structure J, flat surfaces are the simplest ones from intrinsic point of views. On the other hand, from J-action point of views, the most natural surfaces in \bm{C}<SUP>2</SUP> are slant surfaces, i.e., surfaces with constant Wintinger angle. In this paper the author completely classifies flat slant surfaces in \bm{C}<SUP>2</SUP>. The main result states that, beside the totally geodesic ones, there are five large classes of flat slant surfaces in \bm{C}<SUP>2</SUP>. Conversely, every non-totally geodesic flat slant surfaces in \bm{C}<SUP>2</SUP> is locally a surface given by these five classes.
- 社団法人 日本数学会の論文
- 2002-10-01
著者
関連論文
- Characterizing a class of totally real submanifolds of S^6 by their sectional curvatures
- Two equivariant totally real immersions into the nearly Kahler 6-sphere and their characterization
- COMPACT HYPERSURFACES DETERMINED BY A SPECTRAL VARIATIONAL PRINCIPLE
- On normal connection of Kaehler submanifolds
- Lagrangian surfaces in complex Euclidean plane via spherical and hyperbolic curves
- COMPLETE CLASSIFICATION OF LORENTZ SURFACES WITH PARALLEL MEAN CURVATURE VECTOR IN ARBITRARY PSEUDO-EUCLIDEAN SPACE
- Complete classification of parallel surfaces in 4-dimensional Lorentzian space forms
- Lagrangian minimal isometric immersions of a Lorentzian real spaceform into a Lorentzian complex space form
- Biharmonic surfaces in pseudo Euclidean spaces
- On classification of some surfaces of revolution of finite type
- Lagrangian surfaces of constant curvature in complex Euclidean plane
- Representation of flat Lagrangian H-umbilical submanifolds in complex Euclidean spaces
- Local rigidity theorems of 2-type hypersurfaces in a hypersphere : Dedicated to Professor Tadashi Nagano on his 60th birthday
- Maslovian Lagrangian immersions of real space forms into complex space forms
- Complex extensors and Lagrangian submanifolds in complex Euclidean spaces
- Some new obstructions to minimal and Lagrangian isometric immersions Dedicated to Professor Tadashi Nagano on the occasion of his seventieth birthday
- Classification of flat slant surfaces in complex Euclidean plane : In memory of Professor Seiichi Yamaguchi
- A cohomology class for totally real surface in C^2
- Stationary 2-type surfaces in a hypersphere
- Manifolds with vanishing Weyl or Bochner curvature tensor
- Harmonic metrics, harmonic tensors, and Gauss maps