<p>We consider the pseudo-nearly Kähler <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\text {SL}(2,\mathbb {R})\times \text {SL}(2,\mathbb {R})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>SL</mtext> <mo stretchy="false">(</mo> <mn>2</mn> <mo>,</mo> <mi mathvariant="double-struck">R</mi> <mo stretchy="false">)</mo> <mo>×</mo> <mtext>SL</mtext> <mo stretchy="false">(</mo> <mn>2</mn> <mo>,</mo> <mi mathvariant="double-struck">R</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> and we study its Lagrangian submanifolds. We provide examples of Lagrangian submanifolds which do not have an analogue in <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\mathbb {S}^3\times \mathbb {S}^3$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi mathvariant="double-struck">S</mi> </mrow> <mn>3</mn> </msup> <mo>×</mo> <msup> <mrow> <mi mathvariant="double-struck">S</mi> </mrow> <mn>3</mn> </msup> </mrow> </math></EquationSource> </InlineEquation>. We also provide an expression for the automorphism group of <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\text {SL}(2,\mathbb {R})\times \text {SL}(2,\mathbb {R})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>SL</mtext> <mo stretchy="false">(</mo> <mn>2</mn> <mo>,</mo> <mi mathvariant="double-struck">R</mi> <mo stretchy="false">)</mo> <mo>×</mo> <mtext>SL</mtext> <mo stretchy="false">(</mo> <mn>2</mn> <mo>,</mo> <mi mathvariant="double-struck">R</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> with the pseudo-Riemannian nearly Kähler metric. The main result is a complete classification of extrinsically homogeneous Lagrangian submanifolds in this space.</p>

Extrinsically Homogeneous Lagrangian Submanifolds of the Pseudo-Nearly Kähler $\text {SL}(2,\mathbb {R})\times \text {SL}(2,\mathbb {R})$

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2026年7月11日

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Mateo Anarella

摘要

We consider the pseudo-nearly Kähler $\text {SL}(2,\mathbb {R})\times \text {SL}(2,\mathbb {R})$ $SL (2, R) \times SL (2, R)$ and we study its Lagrangian submanifolds. We provide examples of Lagrangian submanifolds which do not have an analogue in $\mathbb {S}^3\times \mathbb {S}^3$ $S^{3} \times S^{3}$ . We also provide an expression for the automorphism group of $\text {SL}(2,\mathbb {R})\times \text {SL}(2,\mathbb {R})$ $SL (2, R) \times SL (2, R)$ with the pseudo-Riemannian nearly Kähler metric. The main result is a complete classification of extrinsically homogeneous Lagrangian submanifolds in this space.

Extrinsically Homogeneous Lagrangian Submanifolds of the Pseudo-Nearly Kähler \(\text {SL}(2,\mathbb {R})\times \text {SL}(2,\mathbb {R})\)

摘要