Almost Complex Surfaces in the Nearly Kähler SL(2,ℝ) × SL(2,ℝ)

The space <inline-formula> <math display="inline"> <semantics> <mrow> <mi>S</mi> <mi>L</mi> <mo>(</mo> <mn>2</mn> <mo>,</mo> <mi mathvariant="double-struck">R</mi> <mo>)</mo&g...

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Main Authors:	Elsa Ghandour, Luc Vrancken
Format:	Article
Language:	English
Published:	MDPI AG 2020-07-01
Series:	Mathematics
Subjects:	submanifold theory nearly Kähler almost complex surface
Online Access:	https://www.mdpi.com/2227-7390/8/7/1160

id	doaj-d6a46183ddf945aba23a3af2fcd3ca52
record_format	Article
spelling	doaj-d6a46183ddf945aba23a3af2fcd3ca522020-11-25T02:59:53ZengMDPI AGMathematics2227-73902020-07-0181160116010.3390/math8071160Almost Complex Surfaces in the Nearly Kähler <b><i>SL</i></b>(<b>2</b>,ℝ) × <b><i>SL</i></b>(<b>2</b>,ℝ)Elsa Ghandour0Luc Vrancken1Faculty of Science, University of Lund, Box 118, 2210 Lund, SwedenLMI-Laboratoire de Mathématiques pour l’Ingénieur, Université Polytechnique Hauts-de-France, Campus du Mont Houy, 59313 Valenciennes, FranceThe space <inline-formula> <math display="inline"> <semantics> <mrow> <mi>S</mi> <mi>L</mi> <mo>(</mo> <mn>2</mn> <mo>,</mo> <mi mathvariant="double-struck">R</mi> <mo>)</mo> <mo>×</mo> <mi>S</mi> <mi>L</mi> <mo>(</mo> <mn>2</mn> <mo>,</mo> <mi mathvariant="double-struck">R</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> admits a natural homogeneous pseudo-Riemannian nearly Kähler structure. We investigate almost complex surfaces in this space. In particular, we obtain a complete classification of the totally geodesic almost complex surfaces and of the almost complex surfaces with parallel second fundamental form.https://www.mdpi.com/2227-7390/8/7/1160submanifold theorynearly Kähleralmost complex surface
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Elsa Ghandour Luc Vrancken
spellingShingle	Elsa Ghandour Luc Vrancken Almost Complex Surfaces in the Nearly Kähler <b><i>SL</i></b>(<b>2</b>,ℝ) × <b><i>SL</i></b>(<b>2</b>,ℝ) Mathematics submanifold theory nearly Kähler almost complex surface
author_facet	Elsa Ghandour Luc Vrancken
author_sort	Elsa Ghandour
title	Almost Complex Surfaces in the Nearly Kähler <b><i>SL</i></b>(<b>2</b>,ℝ) × <b><i>SL</i></b>(<b>2</b>,ℝ)
title_short	Almost Complex Surfaces in the Nearly Kähler <b><i>SL</i></b>(<b>2</b>,ℝ) × <b><i>SL</i></b>(<b>2</b>,ℝ)
title_full	Almost Complex Surfaces in the Nearly Kähler <b><i>SL</i></b>(<b>2</b>,ℝ) × <b><i>SL</i></b>(<b>2</b>,ℝ)
title_fullStr	Almost Complex Surfaces in the Nearly Kähler <b><i>SL</i></b>(<b>2</b>,ℝ) × <b><i>SL</i></b>(<b>2</b>,ℝ)
title_full_unstemmed	Almost Complex Surfaces in the Nearly Kähler <b><i>SL</i></b>(<b>2</b>,ℝ) × <b><i>SL</i></b>(<b>2</b>,ℝ)
title_sort	almost complex surfaces in the nearly kähler <b><i>sl</i></b>(<b>2</b>,ℝ) × <b><i>sl</i></b>(<b>2</b>,ℝ)
publisher	MDPI AG
series	Mathematics
issn	2227-7390
publishDate	2020-07-01
description	The space <inline-formula> <math display="inline"> <semantics> <mrow> <mi>S</mi> <mi>L</mi> <mo>(</mo> <mn>2</mn> <mo>,</mo> <mi mathvariant="double-struck">R</mi> <mo>)</mo> <mo>×</mo> <mi>S</mi> <mi>L</mi> <mo>(</mo> <mn>2</mn> <mo>,</mo> <mi mathvariant="double-struck">R</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> admits a natural homogeneous pseudo-Riemannian nearly Kähler structure. We investigate almost complex surfaces in this space. In particular, we obtain a complete classification of the totally geodesic almost complex surfaces and of the almost complex surfaces with parallel second fundamental form.
topic	submanifold theory nearly Kähler almost complex surface
url	https://www.mdpi.com/2227-7390/8/7/1160
work_keys_str_mv	AT elsaghandour almostcomplexsurfacesinthenearlykahlerbislibb2brbislibb2br AT lucvrancken almostcomplexsurfacesinthenearlykahlerbislibb2brbislibb2br
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Almost Complex Surfaces in the Nearly Kähler <b><i>SL</i></b>(<b>2</b>,ℝ) × <b><i>SL</i></b>(<b>2</b>,ℝ)

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