On Some Weingarten Surfaces in the Special Linear Group SL(2,<inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula>)

We classify Weingarten conoids in the real special linear group <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>SL</mi><mo>(</mo><mn>2</mn><mo>,</mo><...

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Main Author: Marian Ioan Munteanu
Format: Article
Language:English
Published: MDPI AG 2023-11-01
Series:Mathematics
Subjects:
Online Access:https://www.mdpi.com/2227-7390/11/22/4636
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author Marian Ioan Munteanu
author_facet Marian Ioan Munteanu
author_sort Marian Ioan Munteanu
collection DOAJ
description We classify Weingarten conoids in the real special linear group <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>SL</mi><mo>(</mo><mn>2</mn><mo>,</mo><mi mathvariant="double-struck">R</mi><mo>)</mo></mrow></semantics></math></inline-formula>. In particular, there is no linear Weingarten nontrivial conoids in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>SL</mi><mo>(</mo><mn>2</mn><mo>,</mo><mi mathvariant="double-struck">R</mi><mo>)</mo></mrow></semantics></math></inline-formula>. We also prove that the only conoids in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>SL</mi><mo>(</mo><mn>2</mn><mo>,</mo><mi mathvariant="double-struck">R</mi><mo>)</mo></mrow></semantics></math></inline-formula> with constant Gaussian curvature are the flat ones. Finally, we show that any surface that is invariant under left translations of the subgroup <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">N</mi></semantics></math></inline-formula> is a Weingarten surface.
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spelling doaj.art-866877ac1f214b5190a88721265e28142023-11-24T14:54:17ZengMDPI AGMathematics2227-73902023-11-011122463610.3390/math11224636On Some Weingarten Surfaces in the Special Linear Group SL(2,<inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula>)Marian Ioan Munteanu0Faculty of Mathematics, Alexandru Ioan Cuza University of Iasi, Bd. Carol I, n. 11, 700506 Iasi, RomaniaWe classify Weingarten conoids in the real special linear group <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>SL</mi><mo>(</mo><mn>2</mn><mo>,</mo><mi mathvariant="double-struck">R</mi><mo>)</mo></mrow></semantics></math></inline-formula>. In particular, there is no linear Weingarten nontrivial conoids in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>SL</mi><mo>(</mo><mn>2</mn><mo>,</mo><mi mathvariant="double-struck">R</mi><mo>)</mo></mrow></semantics></math></inline-formula>. We also prove that the only conoids in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>SL</mi><mo>(</mo><mn>2</mn><mo>,</mo><mi mathvariant="double-struck">R</mi><mo>)</mo></mrow></semantics></math></inline-formula> with constant Gaussian curvature are the flat ones. Finally, we show that any surface that is invariant under left translations of the subgroup <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">N</mi></semantics></math></inline-formula> is a Weingarten surface.https://www.mdpi.com/2227-7390/11/22/4636rotational surfacesconoids<named-content content-type="inline-formula"><inline-formula><mml:math display="block" id="mm11111111"><mml:semantics><mml:mrow><mml:mi mathvariant="script">N</mml:mi></mml:mrow></mml:semantics></mml:math></inline-formula></named-content>-surfacesWeingarten surfacesspecial linear group
spellingShingle Marian Ioan Munteanu
On Some Weingarten Surfaces in the Special Linear Group SL(2,<inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula>)
Mathematics
rotational surfaces
conoids
<named-content content-type="inline-formula"><inline-formula><mml:math display="block" id="mm11111111"><mml:semantics><mml:mrow><mml:mi mathvariant="script">N</mml:mi></mml:mrow></mml:semantics></mml:math></inline-formula></named-content>-surfaces
Weingarten surfaces
special linear group
title On Some Weingarten Surfaces in the Special Linear Group SL(2,<inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula>)
title_full On Some Weingarten Surfaces in the Special Linear Group SL(2,<inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula>)
title_fullStr On Some Weingarten Surfaces in the Special Linear Group SL(2,<inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula>)
title_full_unstemmed On Some Weingarten Surfaces in the Special Linear Group SL(2,<inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula>)
title_short On Some Weingarten Surfaces in the Special Linear Group SL(2,<inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula>)
title_sort on some weingarten surfaces in the special linear group sl 2 inline formula math display inline semantics mrow mi mathvariant double struck r mi mrow semantics math inline formula
topic rotational surfaces
conoids
<named-content content-type="inline-formula"><inline-formula><mml:math display="block" id="mm11111111"><mml:semantics><mml:mrow><mml:mi mathvariant="script">N</mml:mi></mml:mrow></mml:semantics></mml:math></inline-formula></named-content>-surfaces
Weingarten surfaces
special linear group
url https://www.mdpi.com/2227-7390/11/22/4636
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