Extrinsically homogeneous Lagrangian submanifolds of the pseudo-nearly K\"ahler $\mathrm{SL}(2,\mathbb{R})\times\mathrm{SL}(2,\mathbb{R})$
Résumé
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.
Mots clés
FOS: Mathematics
53C42
2020 Mathematics Subject Classification. 53C42 Nearly Kähler homogeneous manifold six-dimensional Lagrangian extrinsically homogeneous submanifold
2020 Mathematics Subject Classification. 53C42 Nearly Kähler
homogeneous manifold
six-dimensional
Lagrangian
extrinsically homogeneous submanifold
Differential Geometry (math.DG)
Domaines
Géométrie différentielle [math.DG]| Origine | Fichiers produits par l'(les) auteur(s) |
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