Zobrazeno 1 - 10
of 60
pro vyhledávání: '"Leschke, K."'
Publikováno v:
manuscripta math. 140 (2013) 213-236
We define a transformation on harmonic maps from a Riemann surface into the 2-sphere which depends on a complex parameter, the so-called mu-Darboux transformation. In the case when the harmonic map N is the Gauss map of a constant mean curvature surf
Externí odkaz:
http://arxiv.org/abs/1009.5274
Autor:
Leschke, K.
In this note we demonstrate how the analogy between the harmonic Gauss map of a constant mean curvature surface and the harmonic conformal Gauss map of a Willmore surface can be used to obtain results on Willmore surfaces.
Comment: 9 pages
Comment: 9 pages
Externí odkaz:
http://arxiv.org/abs/1003.3371
Autor:
Leschke, K.
For all positive integers n we construct a 1-parameter family of conformal tori of revolution in the 3-sphere with n bulges. These tori arise by Darboux transformations of constant mean curvature tori but do not have constant mean curvature in the 3-
Externí odkaz:
http://arxiv.org/abs/0909.3965
Autor:
Leschke, K., Romon, P.
The multiplier spectral curve of a conformal torus in the 4-sphere is essentially, see arXiv:0712.2311, given by all Darboux transforms of the conformal torus. In the particular case when the conformal immersion is a Hamiltonian stationary torus in E
Externí odkaz:
http://arxiv.org/abs/0806.1848
Publikováno v:
J. Reine Angew. Math. 671 (2012), 1-30
We study the space of conformal immersions of a 2-torus into the 4-sphere. The moduli space of generalized Darboux transforms of such an immersed torus has the structure of a Riemann surface, the spectral curve. This Riemann surface arises as the zer
Externí odkaz:
http://arxiv.org/abs/0712.2311
Autor:
Leschke, K., Pedit, F.
Publikováno v:
Math. Z. (2008) 259: 113-122
In this paper we develop the theory of Willmore sequences for Willmore surfaces in the 4-sphere. We show that under appropriate conditions this sequence has to terminate. In this case the Willmore surface either is the twistor projection of a holomor
Externí odkaz:
http://arxiv.org/abs/math/0610648
We characterize Willmore tori in the 4-sphere with nontrivial normal bundle as Twistor projections of elliptic curves in complex projective space or as inverted minimal tori (with planar ends) in Euclidean 4-space.
Comment: 11 pages
Comment: 11 pages
Externí odkaz:
http://arxiv.org/abs/math/0312421
Autor:
Leschke, K., Pedit, F.
Publikováno v:
J. London Math. Soc (2) 75 (2007), p. 199-212.
We view conformal surfaces in the 4--sphere as quaternionic holomorphic curves in quaternionic projective space. By constructing enveloping and osculating curves, we obtain new holomorphic curves in quaternionic projective space and thus new conforma
Externí odkaz:
http://arxiv.org/abs/math/0306150
Autor:
Leschke, K.
The Willmore energy for Frenet curves in quaternionic projective space is the generalization of the Willmore functional for immersions into the 4-sphere. Critical points of the Willmore energy are called Willmore curves in quaternionic projective spa
Externí odkaz:
http://arxiv.org/abs/math/0209359
The paper develops the fundamentals of quaternionic holomorphic curve theory. The holomorphic functions in this theory are conformal maps from a Riemann surface into the 4-sphere, i.e., the quaternionic projective line. Basic results such as the Riem
Externí odkaz:
http://arxiv.org/abs/math/0012238