Isometric immersions of R² into R⁴ and pertubation of Hopf tori

2003/01/09 by Jose A. Galvez, Pablo Mira, Galvez, Jose A. +1 · 1 citation
Mathematics · #53C40 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C40

paper · pdf · doi:10.48550/arxiv.math/0301075

26 pages, 1 figure

arxiv created 2003/01/09 · arxiv updated 2009/11/30

Abstract

We produce a new general family of flat tori in R⁴, the first one since Bianchi's classical works in the 19th century. To construct these flat tori, obtained via small perturbation of certain Hopf tori in S³, we first present a global description of all isometric immersions of R² into R⁴ with flat normal bundle.

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• Rigidity of Translation Surfaces in the Three-Dimensional Sphere \mathbbS³

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