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Transformations between surfaces in R^4 with flat normal and/or tangent bundles

Angel Montesinos-Amilibia
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Abstract

We exhibit several transformations of surfaces in R^4. First, one that takes a flat surface and gets a surface with flat normal bundle; then, one that takes a surface with flat normal bundle and gets a flat surface; finally, a one-parameter family of transformations on a flat surface with flat normal bundle and gives a flat surface with flat normal bundle. This family satisfies a permutability property.

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Angel Montesinos-Amilibia. 2005-10-24. Transformations between surfaces in R^4 with flat normal and/or tangent bundles. https://arxiv.org/abs/math/0510413

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