COMPLETE CLASSIFICATION OF LORENTZ SURFACES WITH PARALLEL MEAN CURVATURE VECTOR IN ARBITRARY PSEUDO-EUCLIDEAN SPACE
スポンサーリンク
概要
- 論文の詳細を見る
Surfaces with parallel mean curvature vector play important roles in the theory of harmonic maps, differential geometry as well as in physics. Surfaces with parallel mean curvature vector in Riemannian space forms were classified in the early 1970s by Chen and Yau. Recently, space-like surfaces with parallel mean curvature vector in arbitrary indefinite space forms were completely classified by Chen in two papers in 2009. In this paper, we completely classify Lorentz surfaces with parallel mean curvature vector in a pseudo-Euclidean space Ems with arbitrary dimension m and arbitrary index s. Our main result states that there are 23 families of Lorentz surfaces with parallel mean curvature vector in a pseudo-Euclidean m-space Ems . Conversely, every Lorentz surface with parallel mean curvature vector in Ems is obtained from the 23 families.
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