Applications of Quaternionic Holomorphic Geometry to minimal surfaces

• Autorzy: K. Leschke , K. Moriya
• Języki publikacji: EN

Abstrakty

EN

In this paper we give a survey of methods of Quaternionic Holomorphic Geometry and of applications of the theory to minimal surfaces. We discuss recent developments in minimal surface theory using integrable systems. In particular, we give the Lopez–Ros deformation and the simple factor dressing in terms of the Gauss map and the Hopf differential of the minimal surface. We illustrate the results for well–known examples of minimal surfaces, namely the Riemann minimal surfaces and the Costa surface.

• Wydawca: De Gruyter Open
• Czasopismo: Complex Manifolds
• Rocznik: 2016
• Tom: 3
• Numer: 1

Daty

otrzymano

2016-07-01

zaakceptowano

2016-10-13

online

2016-11-16

Twórcy

autor

K. Leschke

• Department of Mathematics, University of Leicester, University Road, Leicester LE1 7RH, United Kingdom

autor

K. Moriya

• Division of Mathematics, Faculty of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba-shi, Ibaraki-ken 305-8571, Japan

Identyfikatory

DOI

10.1515/coma-2016-0015