On Some Weingarten Surfaces in the Special Linear Group SL(2, R )

Marian Ioan Munteanu ()
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Marian Ioan Munteanu: Faculty of Mathematics, Alexandru Ioan Cuza University of Iasi, Bd. Carol I, n. 11, 700506 Iasi, Romania

Mathematics, 2023, vol. 11, issue 22, 1-22

Abstract: We classify Weingarten conoids in the real special linear group SL ( 2 , R ) . In particular, there is no linear Weingarten nontrivial conoids in SL ( 2 , R ) . We also prove that the only conoids in SL ( 2 , R ) with constant Gaussian curvature are the flat ones. Finally, we show that any surface that is invariant under left translations of the subgroup N is a Weingarten surface.

Keywords: rotational surfaces; conoids; N -surfaces; Weingarten surfaces; special linear group (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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