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

Pub Date : 2024-03-03 DOI:10.1002/mana.202300351

Mateo Anarella, J. Van der Veken

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Abstract

In this paper, we study Lagrangian submanifolds of the pseudo-nearly Kähler $SL (2, R) \times SL (2, R)$ . 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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伪近似 Kähler SL(2,R)×SL(2,R)$\mathrm{SL}(2,\mathbb {R})\times \mathrm{SL}(2,\mathbb {R})$ 的完全测地拉格朗日子网格

在本文中，我们研究了伪近似凯勒的拉格朗日子漫空间（Lagrangian submanifolds of the pseudo-nearly Kähler .首先，我们证明了它们分为四个不同的类别，这取决于它们相对于环境空间上的某种近积结构的行为。然后，我们给出了该空间的完全测地拉格朗日子实体的完整分类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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