A Fundamental Theorem for submanifolds of multiproducts of real space forms

2015/02/11 by Marie-Amélie Lawn, Julien Roth, Lawn, Marie-Amélie +1
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.1502.03427

arxiv created 2015/02/11 · arxiv updated 2015/02/12

Abstract

We prove a Bonnet theorem for isometric immersions of submanifolds into the products of an arbitrary number of simply connected real space forms. Then, we prove the existence of associated families of minimal surfaces in such products. Finally, in the case of \mathbbS²×\mathbbS², we give a complex version of the main theorem in terms of the two canonical complex structures of \mathbbS²×\mathbbS².

Citations

• A Bonnet theorem for isometric immersions into products of space forms
• Isometric immersions into products of space forms

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• Minimal Kähler submanifolds in product of space forms
• Spinorial representation of submanifolds in a product of space forms
• Minimal surfaces in the product of two dimensional real space forms endowed with a neutral metric
• Minimal isometric immersions into S² x R and H² x R