Convex decompositions of real projective surfaces. II. Admissible decompositions

Choi, Suhyoung

doi:10.4310/jdg/1214455537

Cited by 29 publications

(86 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…If Σ has no boundary and is convex, then any closed geodesic b is principal (see [19] and [6]). When Σ has boundary diffeomorphic to a circle, we will require each boundary component to be a principal closed geodesic in this paper for convenience.…”

Section: Splitting and Sewing Rp 2 -Orbifoldsmentioning

confidence: 99%

The deformation spaces of convex [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]-structures on 2-orbifolds

Choi¹,

Goldman²

2005

ajm

Self Cite

View full text Add to dashboard Cite

Abstract. We determine that the deformation space of convex real projective structures, that is, projectively flat torsion-free connections with the geodesic convexity property on a compact 2-orbifold of negative Euler characteristic is homeomorphic to a cell of certain dimension. The basic techniques are from Thurston's lecture notes on hyperbolic 2-orbifolds, the previous work of Goldman on convex real projective structures on surfaces, and some classical geometry.

show abstract

Section: Splitting and Sewing Rp 2 -Orbifoldsmentioning

confidence: 99%

The deformation spaces of convex [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]-structures on 2-orbifolds

Choi¹,

Goldman²

2005

ajm

Self Cite

View full text Add to dashboard Cite

show abstract

“…[7], [8], [9]). De plus, si les surfaces convexes sont choisies maximales, cette décomposition est unique.…”

Section: Propriétés éLémentaires Des Homéomorphismes Locauxunclassified

“…le complémentaire d'une droite projective dans RP 2 ), et qu'elle est convexe dans ce plan affine (cf. [8], [14]). Une surface affine est dite homogène si le groupe de ses automorphismes affines agit transitivement sur elle-même.…”

unclassified

Variétés affines radiales de dimension 3

Barbot¹

2000

Bul. Soc. Math. France

View full text Add to dashboard Cite

“…A typical example of such a structure is given by the projectivisation of the tangent bundle of a 2-dimensional real projective orbifold. This family is fairly well-understood, thanks to the classification of compact real projective surfaces (see [11,12,13,14]). Anyway, the flag manifolds we will consider here are of different nature.…”

Section: Theorem a Every Hyperbolic Action Ofγ Is Topologically Conjumentioning

confidence: 99%

Flag structures on Seifert manifolds

Barbot

2001

Geom. Topol.

View full text Add to dashboard Cite

We consider faithful projective actions of a cocompact lattice of SL(2, R) on the projective plane, with the following property: there is a common fixed point, which is a saddle fixed point for every element of infinite order of the the group. Typical examples of such an action are linear actions, ie, when the action arises from a morphism of the group into GL(2, R), viewed as the group of linear transformations of a copy of the affine plane in RP 2 . We prove that in the general situation, such an action is always topologically linearisable, and that the linearisation is Lipschitz if and only if it is projective. This result is obtained through the study of a certain family of flag structures on Seifert manifolds. As a corollary, we deduce some dynamical properties of the transversely affine flows obtained by deformations of horocyclic flows. In particular, these flows are not minimal.

show abstract

Convex decompositions of real projective surfaces. II. Admissible decompositions

Cited by 29 publications

References 14 publications

The deformation spaces of convex [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]-structures on 2-orbifolds

The deformation spaces of convex [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]-structures on 2-orbifolds

Variétés affines radiales de dimension 3

Flag structures on Seifert manifolds

Contact Info

Product

Resources

About