A fundamental theorem for submanifolds of multiproducts of real space forms

作者：Lawn Marie Amelie; Roth Julien

来源：Advances in Geometry, 2017, 17(3): 323-337.

DOI：10.1515/advgeom-2017-0021

• Product spaces
• isometric immersions
• minimal surfaces
• associated families

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 S-2 x S-2, we give a complex version of the main theorem in terms of the two canonical complex structures of S-2 x S-2.

• 出版日期2017-7