Zobrazeno 1 - 10
of 99
pro vyhledávání: '"Hertrich‐Jeromin, U."'
It is shown that a canonical geometric setting of the integrable TED equation is a Kahlerian tangent bundle of an affine manifold. The remarkable multi-dimensional consistency of this 4+4-dimensional dispersionless partial differential equation arise
Externí odkaz:
http://arxiv.org/abs/2402.11779
For CMC surfaces in $3$-dimensional space forms, we relate the moment class of Korevaar--Kusner--Solomon to a second cohomology class arising from the integrable systems theory of isothermic surfaces. In addition, we show that both classes have a var
Externí odkaz:
http://arxiv.org/abs/2401.10618
Publikováno v:
In Journal of Geometry and Physics January 2025 207
Publikováno v:
Proc. London Math. Soc. 126 (2023) 790-836
We provide a convincing discretisation of Demoulin's $\Omega$-surfaces along with their specialisations to Guichard and isothermic surfaces with no loss of integrable structure.
Comment: 40 A4 pages. v2: small changes in response to referee, inc
Comment: 40 A4 pages. v2: small changes in response to referee, inc
Externí odkaz:
http://arxiv.org/abs/2008.01447
Publikováno v:
Beitraege Alg. u. Geom. 60 (2019) 39-55
We discuss results for the Ribaucour transformation of curves or of higher dimensional smooth and discrete submanifolds. In particular, a result for the reduction of the ambient dimension of a submanifold is proved and the notion of Ribaucour coordin
Externí odkaz:
http://arxiv.org/abs/1711.04605
Autor:
Hertrich-Jeromin, U., Honda, A.
We derive a permutability theorem for the Christoffel, Goursat and Darboux transformations of isothermic surfaces. As a consequence we obtain a simple proof of a relation between Darboux pairs of minimal surfaces in Euclidean space, curved flats in t
Externí odkaz:
http://arxiv.org/abs/1602.06682
We demonstrate that every non-tubular channel linear Weingarten surface in Euclidean space is a surface of revolution, hence parallel to a catenoid or a rotational surface of non-zero constant Gauss curvature. We provide explicit parametrizations and
Externí odkaz:
http://arxiv.org/abs/1507.03394
Publikováno v:
Geom. Dedicata 183 (2016) 43-58
A Darboux transformation for polarized space curves is introduced and its properties are studied, in particular, Bianchi permutability. Semi-discrete isothermic surfaces are described as sequences of Darboux transforms of polarized curves in the conf
Externí odkaz:
http://arxiv.org/abs/1506.04730
Publikováno v:
Discrete and Computational Geometry (2014) 52, 612-629
We show that the discrete principal nets in quadrics of constant curvature that have constant mixed area mean curvature can be characterized by the existence of a K\"onigs dual in a concentric quadric.
Comment: 12 pages, 10 figures, pdfLaTeX (pl
Comment: 12 pages, 10 figures, pdfLaTeX (pl
Externí odkaz:
http://arxiv.org/abs/1409.2001
Publikováno v:
Nagoya Math. J. 231, (2018) 55-88
Discrete linear Weingarten surfaces in space forms are characterized as special discrete $\Omega$-nets, a discrete analogue of Demoulin's $\Omega$-surfaces. It is shown that the Lie-geometric deformation of $\Omega$-nets descends to a Lawson transfor
Externí odkaz:
http://arxiv.org/abs/1406.1293