A fundamental theorem for submanifolds of multiproducts of real space forms-Reference-Cited by-同舟云学术

A fundamental theorem for submanifolds of multiproducts of real space forms

Published:2017-07-01 Issue:3 Volume:17 Page:323-337
ISSN:1615-7168
Container-title:Advances in Geometry
language:en
Short-container-title:

Author:

Lawn Marie-Amélie¹,Roth Julien²

Affiliation:

1. Department of Mathematics , Imperial College London , South Kensington Campus , London , SW72AZ United Kingdom

2. LAMA , Université Paris-Est Marne-la-Vallé , Cité Descartes , Champs-sur-Marne, 77454 Marne-la-Vallée cedex 2 , France

Abstract

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 associate families of minimal surfaces in such products. Finally, in the case of 𝕊2 × 𝕊2, we give a complex version of the main theorem in terms of the two canonical complex structures of 𝕊2 × 𝕊2.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

Link

https://www.degruyter.com/document/doi/10.1515/advgeom-2017-0021/pdf

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