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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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Submitted on : Tuesday, March 2, 2021 - 10:13:17 AM
Last modification on : Wednesday, November 3, 2021 - 9:06:35 AM


  • HAL Id : hal-03155854, version 1



Luc Vrancken. Flat almost complex surfaces in the nearly Kähler S3 × S3. XVIII Geometrical Seminar, May 2013, Vrnjacka Bana, Serbia. 24 pp. ⟨hal-03155854⟩



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