A convexity theorem for real projective structures
نویسندگان
چکیده
منابع مشابه
A convexity theorem for real projective structures
Given a finite collection P of convex n-polytopes in RP (n ≥ 2), we consider a real projective manifold M which is obtained by gluing together the polytopes in P along their facets in such a way that the union of any two adjacent polytopes sharing a common facet is convex. We prove that the real projective structure on M is 1. convex if P contains no triangular polytope, and 2. properly convex ...
متن کاملA Real Convexity Theorem for Quasi-hamiltonian Actions
When (M,ω, μ : M → U) is a quasi-hamiltonian U -space with U a compact connected and simply connected Lie group, the intersection of μ(M) with the exponential exp(W) of a closed Weyl alcove W ⊂ u = Lie(U) is homeomorphic, via the exponential map, to a convex polytope of u ([AMM98]). In this paper, we fix an involutive automorphism τ of U such that the involution τ− : u 7→ τ(u) leaves a maximal ...
متن کاملA Schottky Decomposition Theorem for Complex Projective Structures
Let S be a closed orientable surface of genus at least two, and let C be an arbitrary (complex) projective structure on S. We show that there is a decomposition of S into pairs of pants and cylinders such that the restriction of C to each component has an injective developing map and a discrete and faithful holonomy representation. This decomposition implies that every projective structure can ...
متن کاملProjective Convexity in P Implies Grassmann Convexity
In this note we introduce the notion of Grassmann convexity analogous to the wellknown notion of convexity for curves in real projective spaces. We show that the curve in G2,4 osculating to a convex closed curve in P is Grassmann-convex. This proves that the tangent developable (i.e. the hypersurface formed by all tangents) of any convex curve in P has the ‘degree’ equal to 4. Here by ‘degree’ ...
متن کاملConvex Real Projective Structures on Compact Surfaces
The space of inequivalent representations of a compact surface S with χ(S) < 0 as a quotient of a convex domain in RP by a properly discontinuous group of projective transformations is a cell of dimension
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Geometriae Dedicata
سال: 2015
ISSN: 0046-5755,1572-9168
DOI: 10.1007/s10711-015-0125-1