In this paper, we study Lagrangian submanifolds of the pseudo-nearly Kähler $\mathrm{SL}(2,\mathbb {R})\times \mathrm{SL}(2,\mathbb {R})$ . 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.

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Volume297, Issue5

May 2024

Pages 1922-1944

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

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

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