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Article Dans Une Revue Journal of Geometry and Physics Année : 2023

Minimal δ(2)-ideal Lagrangian submanifolds and the quaternionic projective space

Résumé

We construct an explicit map from a generic minimal δ(2)-ideal Lagrangian submanifold of Cn to the quaternionic projective space HPn−1, whose image is either a point or a minimal totally complex surface. A stronger result is obtained for n=3, since the above mentioned map then provides a one-to-one correspondence between minimal δ(2)-ideal Lagrangian submanifolds of C3 and minimal totally complex surfaces in HP2 which are moreover anti-symmetric. Finally, we also show that there is a one-to-one correspondence between such surfaces in HP2 and minimal Lagrangian surfaces in CP2.

Dates et versions

hal-04398729 , version 1 (16-01-2024)

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Kristof Dekimpe, Joeri van der Veken, Luc Vrancken. Minimal δ(2)-ideal Lagrangian submanifolds and the quaternionic projective space. Journal of Geometry and Physics, 2023, 191, pp.104857. ⟨10.1016/j.geomphys.2023.104857⟩. ⟨hal-04398729⟩
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