3 edition of **Convex and concave decomposition of manifolds with real projective structures** found in the catalog.

- 208 Want to read
- 27 Currently reading

Published
**1999** by Société mathématique de France in [Paris, France] .

Written in English

- Convex domains.,
- Geometry, Projective.,
- Manifolds (Mathematics)

**Edition Notes**

Statement | Suhyoung Choi. |

Series | Mémoires de la Société mathématique de France -- nouv. sér., no. 78., Mémoire (Société mathématique de France) -- nouv. sér., no. 78. |

The Physical Object | |
---|---|

Pagination | 102 p. : |

Number of Pages | 102 |

ID Numbers | |

Open Library | OL17702299M |

ISBN 10 | 2856290795 |

In the theory of several complex variables and complex manifolds in mathematics, a Stein manifold is a complex submanifold of the vector space of n complex dimensions. They were introduced by and named after Karl Stein ().A Stein space is similar to a Stein manifold but is allowed to have singularities. Stein spaces are the analogues of affine varieties or affine schemes in algebraic geometry.

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A (flat) affine 3-manifold is a 3-manifold with an atlas of charts to an affine space [equation] with transition maps in the affine transformation group [equation]. We will show that a connected Convex and Concave Decompositions of Affine 3-Manifolds | SpringerLinkAuthor: Suhyoung Choi.

The Convex and Concave Decomposition of Manifolds With Real Projective Structures. Canonical decomposition of manifolds with flat real projective structure into (n-1)-convex manifolds and concave affine manifolds: Authors: Choi, Suhyoung: Publication: eprint arXiv:math/ Publication Date: 04/ Origin: ARXIV: Keywords: Mathematics - Geometric Topology, 57M50 (Primary) 53A20, 53C15 (Secondary) Comment: 76 pages 9.

Canonical decomposition of manifolds with flat real projective structure into (n-1)-convex manifolds and concave affine manifolds Article (PDF Available) · May with 25 Reads How we measure. Convex decompositions of real projective surfaces.

A real protective surface is a surface with a flat real projective structure. A π-annulus is an easy-to-construct real projective annulus Author: Suhyoung Choi. A real protective surface is a surface with a flat real projective structure.

A π-annulus is an easy-to-construct real projective annulus with geodesic boundary. Goldman classiﬁed projective structures on tori. (His senior thesis) Grafting: One can insert this type of annuli into a convex projective surfaces to obtain non-convex projective surfaces.

Theorem 1 (Convex decomposition ()) Given a closed orientable real projective surface of negative Euler characteristic, has a. real projective structure. We outline this paper.

The main tools of this paper are from three long papers Convex and concave decomposition of manifolds with real projective structures book, [15], and [16]. In Section 2, we discuss the basic facts on real projective and a ne structures. In Sectionwe recall the convex and concave decomposition of real projective structures.

We study a properly convex real projective manifold with (possibly empty) compact, strictly convex boundary, and which consists of a compact part plus finitely many convex ends. We study real projective structures on V. We prove that all such structures are left-invariant which means that they are all obtained by the following process: take a representation of Sol in PGL (4, R) with an open orbit Ω in R P 3 ; it induces a projective structure on Sol and, hence, on the left-quotient Γ\ Cited by: 5.

We show that this further implies the existence of a particular type of affine submanifold in M and give a natural decomposition of M into simpler real projective manifolds, some of which are (n − 1)-convex and others are affine, more specifically concave affine. We feel that it is useful to have such decomposition particularly in dimension three.

arXiv:dg-ga/v4 17 Jul The decomposition and classiﬁcation of radiant decomposition of real projective n-manifolds developed earlier.

Then we decompose a 2-convex radiant aﬃne manifold into convex radiant aﬃne manifolds and concave-cone aﬃne manifolds. To do this, we will obtain certain nice geometric objects in. Get this from a library. The Convex and concave decomposition of manifolds with real projective structures.

[Suhyoung Choi]. The ends of convex real projective manifolds and orbifolds Suhyoung Choi KAIST, Daejeon, MSRI, and UC Davis email: [email protected] Jointly with Yves Carrière and David Fried. CONVEX REAL PROJECTIVE STRUCTURES ON COMPACT SURFACES Suppose that A G SL(3, R).

We define λ(A) to be the real eigenvalue of A G SL(3, R) having the smallest absolute value and τ(A) G R as the sum of the other two (possibly unreal) eigenvalues.

We decompose a closed radiant affine \(3\)-manifold into radiant \(2\)-convex affine manifolds and radiant concave affine \(3\)-manifolds along mutually disjoint totally geodesic tori or Klein bottles using the convex and concave decomposition of real projective \(n\)-manifolds developed earlier.

the case n = 3, such components consist of real projective structures on sur-faces. Johnson and Millson [20] showed that there are non-trivial continu-ous deformations of higher-dimensional hyperbolic structures through strictly convex projective structures.

Conversely, one might expect that if. DEFORMATIONS OF CONVEX REAL PROJECTIVE MANIFOLDS AND ORBIFOLDS SUHYOUNGCHOI,GYE-SEONLEE,AND LUDOVICMARQUIS Abstract. In this survey, we study representations of ﬁnitely generated groups into Lie groups, focusing on the deformation spaces of convex real projective structures on closed.

We show that this further implies the existence of a particular type of affine submanifold in M and give a natural decomposition of M into simpler real projective manifolds, some of which are (n − 1)-convex and others are affine, more specifically concave affine.

Canonical decomposition of manifolds with flat real projective structure into (n-1)-convex manifolds and concave affine manifolds. By Suhyoung Choi. more specifically concave affine.

We feel that it is useful to have such decomposition particularly in dimension three. Our result will later aid us to study the geometric and topological Author: Suhyoung Choi.

The convex and concave decomposition of manifolds with real projective structures By Suhyoung Choi Download PDF (8 MB)Author: Suhyoung Choi. Convex and Concave decomposition of manifolds with real projective structures, Mem. Soc. Math. France vol. 78, pp. 1{, The proceedings of the conference on geometric structures, editor, GARC-Lecture Notes No (with Hyuk Kim and Hyunkoo Lee).

The universal cover of an a ne three-manifold with holonomy of in nitely. Convex projective structures on Gromov–Thurston manifolds MICHAEL KAPOVICH We study Gromov–Thurston examples of negatively curved n–manifolds which do not admit metrics of constant sectional curvature.

We show that for each n>3 some of the Gromov–Thurston manifolds admit strictly convex real-projective structures. 53C15, 53C20; 20F06 1 Cited by: In this paper, we initiate and study manifolds which admit a structure defined by a tensor field ϕ of type (1,1) satisfying ϕ^4 ±ϕ^2 = 0.

Many fundamental properties of such manifolds are. A geometric topologist's definition of an affine manifold is a manifold with an atlas of charts to the affine space with affine transition functions; a radiant affine manifold is an affine manifold with a holonomy. Buy Convex Functions and Optimization Methods on Riemannian Manifolds attempt to make accesible to all users of this book some basic computational techniques and implementation of geometric structures.

To further aid the readers,this book also contains a part of the folklore about Riemannian geometry, convex functions and dynamical systems Cited by: The deformation spaces of convex real projective structures The deformation spaces of convex real projective structures on manifolds or orbifolds with ends: openness and closedness Suhyoung Choi Department of Mathematical Science KAIST, Daejeon, South Korea nuevhogarconsulting.com˘schoi (Copies of my lectures are posted) 1/ Nov 21, · We prove that the real projective structure on M is (1) convex if \(\mathcal {P}\) contains no triangular polytope, and (2) properly convex if, in addition, \(\mathcal {P}\) contains a polytope whose dual polytope is thick.

Triangular polytopes and polytopes with thick duals are defined as analogues of triangles and polygons with at least five Cited by: 9. Abstract: In this survey, we study representations of finitely generated groups into Lie groups, focusing on the deformation spaces of convex real projective structures on closed manifolds and orbifolds, with an excursion on projective structures on surfaces.

We survey the basics of the theory of character varieties, geometric structures on orbifolds, and Hilbert nuevhogarconsulting.com by: 3. 2 The Concave-Convex Procedure (CCCP) The key results of CCCP are summarized by Theorems 1,2, and 3.

Theorem 1 shows that any function, subject to weak conditions, can be expressed as the sum of a convex and concave part (this decomposition is not unique). This implies that CCCP can be applied to (almost) any optimization problem. Theorem 1. Abstract: Y.

Benoist proved that if a closed three-manifold M admits an indecomposable convex real projective structure, then M is topologically the union along tori and Klein bottles of finitely many sub-manifolds each of which admits a complete finite volume hyperbolic structure on its interior.

We describe some initial results in the direction of a potential converse to Benoist's theorem. Theorem ([12]). Suppose that Mis a compact real projective 3-manifold with empty or convex boundary that is neither complete a ne nor bihedral. Suppose that M is not 2-convex. Then M h contains a hemispherical or bihedral 3-crescent.

Now, we sketch the process of convex-concave decomposition in [12] which we recall in Sectionin more details:Author: Suhyoung Choi. Convex Functions and Optimization Methods on Riemannian Manifolds by Constantin Udri§te Metric structure of a Riemannian manifold §7.

Completeness of Riemannian manifolds Strongly convex functions on Riemannian manifolds §2. Convex hypersurfaces in Riemannian manifolds This study of properly or strictly convex real projective manifolds introduces notions of parabolic, horosphere and cusp. Results include a Margulis lemma and in the strictly convex case a thick–thin decomposition.

Finite volume cusps are shown to be projectively equivalent to cusps of hyperbolic nuevhogarconsulting.com by: The Structure of Properly Convex Manifolds Sam Ballas (joint with D. Long) University of Pittsburgh Properly convex)less similar What sort of structure do convex projective manifolds have.

Deformations of ﬁnite volume strictly convex manifolds are structurally similar to complete ﬁnite volume hyperbolic real, and positive. In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, each point of an n -dimensional manifold has a neighborhood that is homeomorphic to the Euclidean space of dimension n.

In this more precise terminology, a manifold is referred to as an n-manifold. ON CONVEX PROJECTIVE MANIFOLDS AND CUSPS DARYL COOPER, DARREN LONG, AND STEPHAN TILLMANN Abstract. This study of properly or strictly convex real projective manifolds introduces notions of parabolic, horosphere and cusp.

Results include a Margulis lemma and in the strictly convex case a thick-thin decomposition. To the Internet Archive Community, Time is running out: please help the Internet Archive today.

The average donation is $ If everyone chips in $5, we can keep our website independent, strong and ad-free. Right now, a generous supporter will match your donation 2.

The projective interpretation of the eight 3-dimensional homogeneous geometries. Molnár, Emil How to cite top. MLA; BibTeX; RIS; Molnár, Emil.

"The projective interpretation of the eight 3-dimensional homogeneous geometries." Beiträge zur Algebra und Geometrie (): The convex and concave decomposition of manifolds with real Cited by: The object of this book is to present the basic facts of convex functions, standard dynamical systems, descent numerical algorithms and some computer programs on Riemannian manifolds in a form suitable for applied mathematicians, scientists and engineers.

A convex projective n-manifold is a manifold of the form n, where ˆRPn is properly convex and ˆPGL() is a discrete torsion free subgroup. A (marked) convex projective structure on a manifold M is an identiﬁcation of M with a properly convex manifold (up to equivalence). A marked convex projective structure gives rise to a.In some sense, the novelty of complex geometry may be traced back to this fundamental observation.

It is true that every complex manifold is in particular a real smooth manifold. This is because the complex plane is, after forgetting its complex structure, isomorphic to the real plane.L-CONVEX-CONCAVE SETS IN REAL PROJECTIVE SPACE AND L-DUALITY* A. Khovanskii, D. Novikov We deﬁne a class of L-convex-concave subsets of RPn, where L is a projective sub- space of dimension l in nuevhogarconsulting.com are sets whose sections by any (l+1)-dimensional.