Zobrazeno 1 - 10
of 122
pro vyhledávání: '"Burstall, F"'
Autor:
Burstall, F. E.
We construct harmonic Riemannian submersions that are retractions from symmetric spaces of noncompact type onto their rank-one totally geodesic subspaces. Among the consequences, we prove the existence of a non-constant, globally defined complex-valu
Externí odkaz:
http://arxiv.org/abs/2404.08596
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:
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
Autor:
Burstall, F. E.
Publikováno v:
Bull. London Math. Soc. 51 (2019) 989-994
We characterise the maps into the space of $2$-spheres in $S^n$ that are the conformal Gauss maps of conformal immersions of a surface. In particular, we give an invariant formulation and efficient proof of a characterisation, due to Dorfmeister--Wan
Externí odkaz:
http://arxiv.org/abs/1904.02574
Autor:
Burstall, F. E.
We characterise the canonical elements, in the sense of Burstall--Rawnsley \cite{BurRaw90}, of a compact semisimple Lie algebra and discuss the case of $\mathfrak{so}(n)$ in detail. In so doing, we correct two errors in Burstall et al. \cite{BurEscFe
Externí odkaz:
http://arxiv.org/abs/1811.12041
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
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:
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
Autor:
Burstall, F. E., Santos, S. D.
Publikováno v:
Geom. Dedicata 172 (2014) 191-205
Isothermic surfaces in $S^n$ are characterised by the existence of a pencil $\nabla^t$ of flat connections. Such a surface is special of type $d$ if there is a family $p(t)$ of $\nabla^t$-parallel sections whose dependence on the spectral parameter $
Externí odkaz:
http://arxiv.org/abs/1301.0447
Publikováno v:
manuscripta math. 140 (2013) 213-236
We define a transformation on harmonic maps from a Riemann surface into the 2-sphere which depends on a complex parameter, the so-called mu-Darboux transformation. In the case when the harmonic map N is the Gauss map of a constant mean curvature surf
Externí odkaz:
http://arxiv.org/abs/1009.5274