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Multi-helicoidal euclidean submanifolds of constant sectional curvature.
| Content Provider | CiteSeerX |
|---|---|
| Author | Ripoll, Jaime Tojeiro, Ruy |
| Abstract | Abstract. We classify n-dimensional multi-helicoidal submanifolds of nonzero con-stant sectional curvature and cohomogeneity one in the Euclidean space R2n−1, that is, n-dimensional submanifolds of nonzero constant sectional curvature in R2n−1 that are invariant under the action of an (n − 1)-parameter subgroup of isome-tries of R2n−1 with no pure translations. This is accomplished by first giving a complete description of all these subgroups and then deriving a multidimensional version of a lemma due to Bour. We also prove that such submanifolds are precisely the ones that correspond to solutions of the generalized sine-Gordon and elliptic sinh-Gordon equations that are invariant by an (n − 1)-dimensional subgroup of translations of the symmetry group of these equations. |
| File Format | |
| Access Restriction | Open |
| Subject Keyword | Constant Sectional Curvature Multi-helicoidal Euclidean Submanifolds Elliptic Sinh-gordon Equation Generalized Sine-gordon Nonzero Con-stant Sectional Curvature Multidimensional Version Parameter Subgroup Euclidean Space R2n Nonzero Constant Sectional Curvature Symmetry Group Complete Description Dimensional Subgroup N-dimensional Submanifolds N-dimensional Multi-helicoidal Submanifolds Pure Translation |
| Content Type | Text |
| Resource Type | Article |
