Totally geodesic Lagrangian submanifolds of the pseudo‐nearly Kähler SL(2,R)×SL(2,R)$\mathrm{SL}(2,\mathbb {R})\times \mathrm{SL}(2,\mathbb {R})$

Mateo Anarella and J. Van der Veken

Mathematische Nachrichten, 2024, vol. 297, issue 5, 1922-1944

Abstract: In this paper, we study Lagrangian submanifolds of the pseudo‐nearly Kähler SL(2,R)×SL(2,R)$\mathrm{SL}(2,\mathbb {R})\times \mathrm{SL}(2,\mathbb {R})$. First, we show that they split into four different classes depending on their behavior with respect to a certain almost product structure on the ambient space. Then, we give a complete classification of totally geodesic Lagrangian submanifolds of this space.

Date: 2024
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https://doi.org/10.1002/mana.202300351

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