Search results

{{Short description|An identity between theta functions of Riemann surfaces}} ...ay's trisecant identity''' is an identity between [[theta function]]s of [[Riemann surface]]s introduced by {{harvs|txt|last=Fay|authorlink=John David Fay|yea ...

...ich are in fact [[quartic curve]]s over {{tmath|\mathbb{C} }}, and quartic surfaces over {{tmath|\mathbb{R} }}. For instance, the [[Klein quartic]] is a ''real ==Special quartic surfaces== ...

...wedge \varphi=0</math> (which is vacuous in Hitchin's original set-up on [[Riemann surface]]s) was introduced later by [[Carlos Simpson]].<ref name="simpson"> ...omorphic vector bundle ''E'' is over a [[compact (mathematics)|compact]] [[Riemann surface]]. Further, Hitchin's paper mostly discusses the case where the vec ...

...ce (topology)#Classification of closed surfaces|classification theorem for surfaces]] states that every [[compact space|compact]] [[connected space|connected]] ...&nbsp;2&nbsp;−&nbsp;2''g'' for [[Surface_(topology)#Closed_surfaces|closed surfaces]], where ''g'' is the genus. ...

...of particular importance in [[Riemann surface]] theory, in connection with surfaces with maximal [[symmetry]], namely the [[Hurwitz surface]]s.<ref>{{citation | title = On the geometry of Hurwitz surfaces ...

...itated at the University of Bonn with a thesis on the length spectrum of [[Riemann surface]]s. Buser is known for his construction of curved isospectral surfaces (published in 1986 and 1988). His 1988 construction led to a negative solut ...

...i. Publ., Teaneck, NJ | series=Proceedings of the First College on Riemann Surfaces held in Trieste, November 9–December 18, 1987 | isbn=9789971509026 |mr=108 ...

...''. These include analogs to physical spaces, like flat planes, and curved surfaces like spheres, cylinders, and cones, which can be infinite or finite. Some t ...iemannian surfaces]]. (Not to be confused with [[Riemann surfaces]].) Some surfaces are [[Embedding|embedded]] in [[three-dimensional Euclidean space]] or some ...

...=Matthias | last=Weber | title= Kepler's small stellated dodecahedron as a Riemann surface| journal = Pacific J. Math.| volume = 220| year=2005 | pages=167–18 ...hed cover|triple cover]] of the sphere branched in 12 points, and is the [[Riemann surface]] associated to the [[small stellated dodecahedron]]. It has genus ...

In [[mathematics]], '''systolic inequalities for curves on surfaces''' were first studied by [[Charles Loewner]] in 1949<!-- That should be lis ...ained by Buser and Sarnak. Namely, they exhibited arithmetic hyperbolic [[Riemann surface]]s with systole behaving as a constant times <math>\log (g)</math>. ...

[[Image:Riemann sqrt.svg|thumb|right|[[Riemann surface]] for the function ''f''(''z'')&nbsp;=&nbsp;{{radic|''z''}}, shown ...Riemann surface]]s, and to analyze maps between surfaces, such as by the [[Riemann–Hurwitz formula]]. ...

...re "almost coverings" in some well defined sense. It applies to bordered [[Riemann surface]]s equipped with conformal [[Riemannian metric]]s. ...bordered Riemann surface'' ''X'' can be defined as a region on a [[compact Riemann surface]] whose boundary ∂''X'' consists of finitely many disjoint Jordan c ...

.... With [[Horst Knörrer]] and [[Eugene Trubowitz]], Feldman has worked on [[Riemann surface]]s of infinite genus. With [[Gunther Uhlmann]] he has written a boo ...ks/about/Riemann_Surfaces_of_Infinite_Genus.html?id=e8WzQmBptRUC ''Riemann Surfaces of Infinite Genus''], AMS (American Mathematical Society) 2003 ...

...=Raoul|authorlink2=Raoul Bott| title=The Yang-Mills equations over Riemann surfaces|journal=[[Philosophical Transactions of the Royal Society A| Philosophical ...

...solutkrümmung immersierter Flächen'' (Total absolute curvature of immersed surfaces). Since 1986 he is professor at [[TU Berlin]].<ref name=homepage/> ...it, Franz|author2=Pinkall, Ulrich|chapter=Quaternionic analysis on Riemann surfaces and differential geometry|title=Doc. Math. (Bielefeld) Extra Vol. ICM Berli ...

|title=Determinants of Cauchy-Riemann operators over a Riemann surface |doi=10.1007/BF01086022 ...ages= 31–34|s2cid=122340883 }}</ref> for certain elliptic operators over a Riemann surface, and generalized to higher-dimensional manifolds by [[Jean-Michel B ...

== Minimal surfaces == * [[Holomorphic map]]s from [[Kähler manifold]]s with values in a [[Riemann surface]] are harmonic morphisms. ...

Stationary fluid films form surfaces of [[Minimal surface|minimal surface area]], leading to the [[Plateau probl ...ensor|curvature tensor]], <math>B^{\alpha }_{\beta }</math> be the mixed [[Riemann curvature tensor|curvature tensor]] and <math>B^{\alpha }_{\alpha }</math> ...

[[File:RiemannKugel.svg|thumb|right|The Riemann sphere can be visualized as the complex number plane wrapped around a spher ...math> onto the points <math>\alpha</math> and <math>\beta</math> of the '''Riemann sphere''' - connect <math>P(\infty)</math> with A or B by a line and determ ...

...t [[Riemann surface]] called its smooth completion. The projection of the Riemann surface to <math>\mathbb{C}\mathbb{P}^1</math> is 2-to-1 over the singular [[Category:Riemann surfaces]] ...