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Flat Almost Complex Surfaces in the Homogeneous Nearly Kähler S3×S3

Bart Dioos 1 Haizhong Li 2 Hui Ma 2 Luc Vrancken 1, 3
1 KU Leuven - Catholic University of Leuven - Katholieke Universiteit Leuven
2 THU - Tsinghua University [Beijing]
3 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015
Abstract : By employing a nice adapted frame we prove a Bonnet-type existence and uniqueness theorem for almost complex surfaces in the homogeneous nearly Kähler manifold S3×S3. The proof uses a local correspondence between almost complex surfaces in S3×S3 and surfaces in R3 that satisfy the Wente H-surface equation. Furthermore we give a complete classification of flat almost complex surfaces in the homogeneous nearly Kähler S3×S3.
Keywords : Almost complex surface flat surface nearly Kähler manifold
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https://hal-uphf.archives-ouvertes.fr/hal-03148536
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Submitted on : Monday, February 22, 2021 - 12:19:15 PM
Last modification on : Tuesday, October 19, 2021 - 6:38:17 PM

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UNIV-VALENCIENNES | INSMI | CNRS | LAMAV

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Bart Dioos, Haizhong Li, Hui Ma, Luc Vrancken. Flat Almost Complex Surfaces in the Homogeneous Nearly Kähler S3×S3. Results in Mathematics, Springer Verlag, 2018, 73 (1), 24 pp. ⟨10.1007/s00025-018-0784-y⟩. ⟨hal-03148536⟩

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