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Flat almost complex surfaces in the nearly Kähler S3 × S3

Abstract : In this talk we show how to study almost complex submanifolds of S3 × S3. Compact 6-dimensional non-K¨ahler nearly K¨ahler manifolds do not admit 4-dimensional almost complex submanifolds, so the almost complex submanifolds are surfaces. Previously, a classification of the totally geodesic almost complex surfaces has been obtained as well as the result that an almost complex immersion of a topological 2 sphere is necessary totally geodesic. In this lecture we will show how to obtain a classification, as well as explicit expressions of all almost complex flat surfaces.
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https://hal-uphf.archives-ouvertes.fr/hal-03155888
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Submitted on : Tuesday, March 2, 2021 - 10:23:05 AM
Last modification on : Tuesday, October 19, 2021 - 6:38:17 PM

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  • HAL Id : hal-03155888, version 1

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Luc Vrancken. Flat almost complex surfaces in the nearly Kähler S3 × S3. Kobe-Leuven workshop on Geometry and Integrable systems, Jul 2014, Leuven, Belgium. 24 pp. ⟨hal-03155888⟩

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