2011/03/12 by Eduardo Hulett, Hulett, Eduardo
Mathematics · Physics and Astronomy · #53C42 #53C43 #53C50 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1103.2485
openalex publication_date 2011/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider conformal immersions of Riemann surfaces in \bbS4 and study their Gauss maps with values in the Grassmann bundle F = SO5/T2 → \mathbbS4. The energy of maps from Riemann surfaces into F is considered with respect to the normal metric on the target and immersions with harmonic Gauss maps are characterized. We also show that the normal-harmonic map equation for Gauss maps is a completely integrable system, thus giving a partial answer of a question posed by Y. Ohnita in \citeohnita. Associated \mathbbS1-families of parallel mean curvature immersions in \mathbbS4 are considered. A lower bound of the normal energy of Gauss maps is obtained in terms of the genus of the surface.