# Lagrangian submanifolds with constant angle functions of the nearly Kähler S3 × S3

Abstract : We study Lagrangian submanifolds of the nearly Kähler S3 × S3 with respect to their so called angle functions. We show that if all angle functions are constant, then the submanifold is either totally geodesic or has constant sectional curvature and there is a classification theorem that follows from Dioos et al. (2018). Moreover, we show that if precisely one angle function is constant, then it must be equal to 0, π3 or 2π3 . Using then two remarkable constructions together with the classification of Lagrangian submanifolds of which the first component has nowhere maximal rank from, Bektaş et al. (2018), we obtain a classification of such Lagrangian submanifolds
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https://hal-uphf.archives-ouvertes.fr/hal-03233861
Contributor : Frédéric Pruvost Connect in order to contact the contributor
Submitted on : Tuesday, May 25, 2021 - 10:12:44 AM
Last modification on : Wednesday, July 13, 2022 - 11:23:54 AM

### Citation

Burcu Bektaş, Marilena Moruz, Joeri van Der Veken, Luc Vrancken. Lagrangian submanifolds with constant angle functions of the nearly Kähler S3 × S3. Journal of Geometry and Physics, Elsevier, 2018, 127, pp.1-13. ⟨10.1016/j.geomphys.2018.01.011⟩. ⟨hal-03233861⟩

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