arXiv math/06010622006-01-18math.DG

Orthogonal curvilinear coordinate systems corresponding to singular spectral curves

A. E. Mironov, I. A. Taimanov

备注：: 20 pages, 7 figures, minor typos corrected (first time the revised version was submiited in Russian)
发表信息：: Proc. Steklov Inst. Math. 255 (2006), 169-184

英文摘要：

We study the limiting case of the Krichever construction of orthogonal curvilinear coordinate systems when the spectral curve becomes singular. We show that the case when the curve is reducible and all its irreducible components are rational curves the construction procedure reduces to solving systems of linear equations and simple computations with elementary functions. Therewith we demonstrate how such well-known coordinate systems as the polar coordinates, the cylindrical coordinates in the three-space, and the spherical coordinates in the Euclidean spaces fit in this scheme.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

常曲率空间中的正交曲线坐标系

On orthogonal curvilinear coordinate systems in constant curvature spaces

本文提出一种修改自 Krichever 方法的构造方法，用于在常曲率空间中生成 $n$-正交坐标系，并在二维球面和双曲平面上给出了谱曲线可约时的实例验证。

2024-11-10math.DG

正交曲线坐标系与可约谱曲线上无挠层

Orthogonal curvilinear coordinate systems and torsion-free sheaves over reducible spectral curves

本文利用有限间隙积分方法，在欧几里得空间中构造了与可约奇异谱曲线上秩一无挠层相对应的正交曲线坐标系。

2023-08-07math.DGnlin.SI

From Ramond Fermions to Lame Equations for Orthogonal Curvilinear Coordinates

We show how Ramond free neutral Fermi fields lead to a $τ$-function theory of BKP type which describes iso-orthogonal deformations of systems of ortogonal curvilinear coordinates. We also provide a vertex operator representation for the classical Ribaucour transformation.

1998-05-20hep-thmath-phmath.DG

Curvilinear coordinates on generic conformally flat hypersurfaces and constant curvature 2-metrics

There is a one-to-one correspondence between associated families of generic conformally flat (local-)hypersurfaces in 4-dimensional space forms and conformally flat 3-metrics with the Guichard condition. In this paper, we study the space of conformally flat 3-metrics with the Guichard condition: for a conformally flat 3-metric with the Guichard condition in the interior of the space, an evolution of orthogonal (local-) Riemannian $2$-metrics with constant Gauss curvature $-1$ is determined; for a $2$-metric belonging to a certain class of orthogonal analytic $2$-metrics with constant Gauss cur…

2016-08-16math.DG

Real square roots of matrices: differential properties in semi-simple, symmetric and orthogonal cases

We study the differential and metric structures of the set of real square roots of a non-singular real matrix, under the assumption that the matrix and its square roots are semi-simple, or symmetric, or orthogonal.

2020-10-29math.DG

Orthogonal Higgs bundles with singular spectral curves

We examine Higgs bundles for non-compact real forms of SO(4,C) and the isogenous complex group SL(2,C)XSL(2,C). This involves a study of non-regular fibers in the corresponding Hitchin fibrations and provides interesting examples of non-abelian spectral data.

2020-08-04math.AGmath.DG

更多相关论文收起更多论文

$\mathfrak{sl}(2)$-type singular fibres of the symplectic and odd orthogonal Hitchin system

We define and parametrise so-called $\mathfrak{sl}(2)$-type fibres of the $\mathsf{Sp}(2n,\mathbb{C})$- and $\mathsf{SO}(2n+1,\mathbb{C})$-Hitchin system. These are (singular) Hitchin fibres, where the spectral curve induces a two-sheeted covering of a second Riemann surface $Y$. This identifies the $\mathfrak{sl}(2)$-type Hitchin fibres with fibres of an $\mathsf{SL}(2,\mathbb{C})$- respectively $\mathsf{PSL}(2,\mathbb{C})$-Hitchin map on $Y$. We give a stratification of these singular spaces by semi-abelian spectral data, study their irreducible components and obtain a global description of …

2021-11-05math.AGmath.DG

Orthogonal Bianchi B stiff fluids close to the initial singularity

In our previous article [Rad16], we investigated the asymptotic behaviour of orthogonal Bianchi class B perfect fluids close to the initial singularity and proved the Strong Cosmic Censorship conjecture in this setting. In several of the statements, the case of a stiff fluid had to be excluded. The present paper fills this gap. We work in expansion-normalised variables introduced by Hewitt-Wainwright and find that solutions converge, but show a convergence behaviour very different from the non-stiff case: All solutions tend to limit points in the two-dimensional Jacobs set. A set of full measu…

2017-12-11gr-qcmath-phmath.DG

正交李代数的Rankin-Cohen括号与双线性共形不变微分算子

Rankin-Cohen brackets for orthogonal Lie algebras and bilinear conformally invariant differential operators

本文利用代数傅里叶变换的李理论方法，分类了正交李代数情形下标量广义Verma模对角分支规则中的奇异向量，并应用于分类共形球面上的双线性共形不变微分算子。

2024-02-12math.APmath.DGmath.RT