Examples of constant mean curvature immersions of the 3-sphere into euclidean 4-space

Embedded Constant Mean Curvature Surfaces in Euclidean Three-space

In this paper we refine the construction and related estimates for complete Constant Mean Curvature surfaces in Euclidean three-space developed in [12] by adopting the more precise and powerful version of the methodology which was developed in [16]. As a consequence we remove the severe restrictions in establishing embeddedness for complete Constant Mean Curvature surfaces in [12] and we produc...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Constant Mean Curvature Surfaces in Euclidean and Minkowski 3-spaces

Spacelike constant mean curvature surfaces in Minkowski 3-space L have an infinite dimensional generalized Weierstrass representation. This is analogous to that given by Dorfmeister, Pedit and Wu for constant mean curvature surfaces in Euclidean space, replacing the group SU(2) with SU(1, 1). The non-compactness of the latter group, however, means that the Iwasawa decomposition of the loop grou...

M ar 2 00 3 Immersions of Arbitrary Constant Mean Curvature in Hyperbolic Space H 3 ( − 1 )

Our work studies immersions of arbitrary constant mean curvature in H3(−1), as integrable surfaces (i.e., associate families of surfaces). We first present new results related to isometric deformations within this category of surfaces. Next, we give a Weierstrass type representation formula for these immersions. Ultimately, we discuss correspondences between such immersions in Euclidean 3-space...

Mean Curvature of Riemannian Immersions

1. Let M and M' denote complete riemannian manifolds of dimension n and m respectively, and suppose that M is compact and oriented. For simplicity we assume that both manifolds and their metrics are smooth (i.e. of class C). In terms of local co-ordinates (x, x, ...,x") on M and local co-ordinates (y,y, •••,/") on M', the riemannian metrics are written ds = gtJ dx l dx, ds' = g'aP dy* dy * wher...