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... > topology > algebraic topology > manifold > differentiable manifold > complex manifold > Riemann surface > Bolza surface
... > geometry > topological space > manifold > differentiable manifold > complex manifold > Riemann surface > Bolza surface
... > geometry > differential geometry > differentiable manifold > complex manifold > Riemann surface > Bolza surface
... > topology > differential topology > differentiable manifold > complex manifold > Riemann surface > Bolza surface
geometry > complex geometry > complex manifold > Riemann surface > Bolza surface
geometry > differential geometry > systolic geometry > Bolza surface
mathematical analysis > functional analysis > geometry of numbers > systolic geometry > Bolza surface
number > number theory > geometry of numbers > systolic geometry > Bolza surface
geometry > discrete geometry > geometry of numbers > systolic geometry > Bolza surface
... > number > real number > Diophantine approximation > geometry of numbers > systolic geometry > Bolza surface
geometry > topological space > metric space > systolic geometry > Bolza surface

Preferred term

Bolza surface  

Definition

  • In mathematics, the Bolza surface, alternatively, complex algebraic Bolza curve (introduced by Oskar Bolza (1887)), is a compact Riemann surface of genus with the highest possible order of the conformal automorphism group in this genus, namely of order 48 (the general linear group of matrices over the finite field ). The full automorphism group (including reflections) is the semi-direct product of order 96. An affine model for the Bolza surface can be obtained as the locus of the equation
    in . The Bolza surface is the smooth completion of the affine curve. Of all genus hyperbolic surfaces, the Bolza surface maximizes the length of the systole (Schmutz 1993). As a hyperelliptic Riemann surface, it arises as the ramified double cover of the Riemann sphere, with ramification locus at the six vertices of a regular octahedron inscribed in the sphere, as can be readily seen from the equation above. The Bolza surface has attracted the attention of physicists, as it provides a relatively simple model for quantum chaos; in this context, it is usually referred to as the Hadamard–Gutzwiller model. The spectral theory of the Laplace–Beltrami operator acting on functions on the Bolza surface is of interest to both mathematicians and physicists, since the surface is conjectured to maximize the first positive eigenvalue of the Laplacian among all compact, closed Riemann surfaces of genus with constant negative curvature.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Bolza_surface)

Broader concept

Entry terms

  • complex algebraic Bolza curve

In other languages

URI

http://data.loterre.fr/ark:/67375/PSR-CJN9CKDM-Q

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RDF/XML TURTLE JSON-LD Created 7/21/23, last modified 10/18/24