Isometric immersions of R^2 into R^4 and pertubation of Hopf tori

Details Isometric immersions of R^2 into R^4 and pertubation of Hopf tori Isometric immersions of R^2 into R^4 and pertubation of Hopf tori

2003-01-09

arxiv.org/abs/math/0301075v1

Mathematics

Differential Geometry

26 pages, 1 figure

Scientific paper

We produce a new general family of flat tori in R^4, 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 S^3, we first present a
global description of all isometric immersions of R^2 into R^4 with flat normal
bundle.

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