An analogue of minimal surface theory in SL(n,C)/SU(n)

2000/08/02 by Masatoshi Kokubu, Kokubu, Masatoshi, Masaro Takahashi +5
Mathematics · #53A07 #53A10 #53A35 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG #msc:53A07 #msc:53A10 #msc:53A35

paper · pdf · doi:10.48550/arxiv.math/0008016

25 pages

openalex publication_date 2000/08/02 · arxiv created 2001/07/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We shall discuss the class of surfaces with holomorphic right Gauss maps in non-compact duals of compact semisimple Lie groups (e.g. SL(n,C)/SU(n)), which contains minimal surfaces in Rⁿ and constant mean curvature 1 surfaces in H³. A Weierstrass type representation formula, and a Chern-Osserman type inequality for such surfaces are given.

Related

• Minimal surfaces that attain equality in the Chern-Osserman inequality
• Spinorial representation of submanifolds in SL_n(ℂ)/SU(n)
• Unstable minimal surfaces in symmetric spaces of non-compact type
• Minimal Surfaces in the Four-Dimensional Euclidean Space
• The Gauss map of surfaces in ~PSL₂(R)