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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 - 10:25:33 AM
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  • HAL Id : hal-03155901, version 1



Luc Vrancken. Flat almost complex surfaces in the nearly Kähler S3 × S3. Riemannian Geometry and Applications Engineering and Economics-RIGA 2014, May 2014, Bucharest, Romania. 24 pp. ⟨hal-03155901⟩



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