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Extrinsically homogeneous Lagrangian submanifolds of the pseudo-nearly Kähler $\mathrm{SL}(2,\mathbb{R})\times\mathrm{SL}(2,\mathbb{R})$
Published 18 Mar 2024 in math.DG | (2403.11962v1)
Abstract: We consider the pseudo-nearly K\"ahler $\mathrm{SL}(2,\mathbb{R})\times\mathrm{SL}(2,\mathbb{R})$ and we study its Lagrangian submanifolds. We provide examples of Lagrangian submanifolds which do not have an analogue in $\mathbb{S}3\times\mathbb{S}3$. We also provide an expression for the isometry group of $\mathrm{SL}(2,\mathbb{R})\times\mathrm{SL}(2,\mathbb{R})$ with the pseudo-Riemannian nearly K\"ahler metric. The main result is a complete classification of extrinsically homogeneous Lagrangian submanifolds in this space.
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