# Manifolds

Xem 1-20 trên 115 kết quả Manifolds
• ### Đề tài " Manifolds with positive curvature operators are space forms "

The Ricci ﬂow was introduced by Hamilton in 1982 [H1] in order to prove that a compact three-manifold admitting a Riemannian metric of positive Ricci curvature is a spherical space form. In dimension four Hamilton showed that compact four-manifolds with positive curvature operators are spherical space forms as well [H2]. More generally, the same conclusion holds for compact four-manifolds with 2-positive curvature operators [Che]. Recall that a curvature operator is called 2-positive, if the sum of its two smallest eigenvalues is positive. ...

• ### Đề tài " Two dimensional compact simple Riemannian manifolds are boundary distance rigid "

We prove that knowing the lengths of geodesics joining points of the boundary of a two-dimensional, compact, simple Riemannian manifold with boundary, we can determine uniquely the Riemannian metric up to the natural obstruction. 1. Introduction and statement of the results Let (M, g) be a compact Riemannian manifold with boundary ∂M . Let dg (x, y) denote the geodesic distance between x and y. The inverse problem we address in this paper is whether we can determine the Riemannian metric g knowing dg (x, y) for any x ∈ ∂M , y ∈ ∂M . ...

• ### Manifolds and Differential Geometry

Classical differential geometry is the approach to geometry that takes full advantage of the introduction of numerical coordinates into a geometric space. This use of coordinates in geometry was the essential insight of Rene Descartes that allowed the invention of analytic geometry and paved the way for modern differential geometry. The basic object in differential geometry (and differential topology) is the smooth manifold. This is a topological space on which a sufficiently nice family of coordinate systems or "charts" is defined.

• ### Đề tài " The space of embedded minimal surfaces of fixed genus in a 3-manifold III; Planar domains "

Annals of Mathematics This paper is the third in a series where we describe the space of all embedded minimal surfaces of ﬁxed genus in a ﬁxed (but arbitrary) closed 3-manifold. In [CM3]–[CM5] we describe the case where the surfaces are topologically disks on any ﬁxed small scale. Although the focus of this paper, general planar domains, is more in line with [CM6], we will prove a result here (namely, Corollary III.

• ### Hot Runner Technology - Peter Unger

Hot Runner Technology has many contents: Introduction, Basic Aspects of Heat Technology, Introduction of Hot Runner Components, Heating of Hot Runner Manifold Blocks, Heating of Hot Runner Nozzles, Measurement and Control of Temperature, Material Behavior under Mechanical Load, Corrosion and Wear, Screw Connections and Material Selection for Elevated Temperatures, Basic Aspects of Plastics Technology, Maintenance and Storage of Hot Runner Molds.

• ### Đề tài " The space of embedded minimal surfaces of fixed genus in a 3-manifold I; Estimates off the axis for disks "

This paper is the ﬁrst in a series where we describe the space of all embedded minimal surfaces of ﬁxed genus in a ﬁxed (but arbitrary) closed Riemannian 3-manifold. The key for understanding such surfaces is to understand the local structure in a ball and in particular the structure of an embedded minimal disk in a ball in R3 (with the ﬂat metric). This study is undertaken here and completed in [CM6]. These local results are then applied in [CM7] where we describe the general structure of ﬁxed genus surfaces in 3-manifolds. There are two local models for...

• ### Đề tài " Propagation of singularities for the wave equation on manifolds with corners "

In this paper we describe the propagation of C ∞ and Sobolev singularities for the wave equation on C ∞ manifolds with corners M equipped with a Rie2 1 mannian metric g. That is, for X = M × Rt , P = Dt − ∆M , and u ∈ Hloc (X) solving P u = 0 with homogeneous Dirichlet or Neumann boundary conditions, we show that WFb (u) is a union of maximally extended generalized broken bicharacteristics. This result is a C ∞ counterpart of Lebeau’s results for the propagation of analytic singularities on real analytic manifolds with...

• ### Ebook A first course in general relativity (2nd edition): Part 1

(BQ) Part 1 book "A first course in general relativity" has contents: Special relativity, vector analysis in special relativity, tensor analysis in special relativity, perfect fluids in special relativity, preface to curvature, curved manifolds.

• ### Báo cáo toán học: " Semi-invariant warped product submanifolds of cosymplectic manifolds"

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học được đăng trên tạp chí toán học quốc tế đề tài: Semi-invariant warped product submanifolds of cosymplectic manifolds

• ### Đề tài " Large Riemannian manifolds which are flexible "

For each k ∈ Z, we construct a uniformly contractible metric on Euclidean space which is not mod k hypereuclidean. We also construct a pair of uniformly contractible Riemannian metrics on Rn , n ≥ 11, so that the resulting manifolds Z and Z are bounded homotopy equivalent by a homotopy equivalence which is not boundedly close to a homeomorphism. We show that for these lf spaces the C ∗ -algebra assembly map K∗ (Z) → K∗ (C ∗ (Z)) from locally ﬁnite K-homology to the K-theory of the bounded propagation algebra is not a monomorphism ...

• ### Đề tài " Holomorphic disks and topological invariants for closed three-manifolds "

Holomorphic disks and topological invariants for closed three-manifolds ´ ´ ´ By Peter Ozsvath and Zoltan Szabo* Abstract The aim of this article is to introduce certain topological invariants for closed, oriented three-manifolds Y , equipped with a Spinc structure. Given a Heegaard splitting of Y = U0 ∪Σ U1 , these theories are variants of the Lagrangian Floer homology for the g-fold symmetric product of Σ relative to certain totally real subspaces associated to U0 and U1 . 1. Introduction Let Y be a connected, closed, oriented three-manifold, equipped with a Spin structure s. ...

• ### Đề tài " Numerical characterization of the K¨ahler cone of a compact K¨ahler manifold "

The goal of this work is to give a precise numerical description of the K¨hler cone of a compact K¨hler manifold. Our main result states that the a a K¨hler cone depends only on the intersection form of the cohomology ring, the a Hodge structure and the homology classes of analytic cycles: if X is a compact K¨hler manifold, the K¨hler cone K of X is one of the connected components of a a the set P of real (1, 1)-cohomology classes {α} which are numerically positive on analytic cycles, i.e. Y αp 0 for every irreducible analytic...

• ### Đề tài " The space of embedded minimal surfaces of fixed genus in a 3-manifold II; Estimates off the axis for disks "

The space of embedded minimal surfaces of ﬁxed genus in a 3-manifold II; Multi-valued graphs in disks By Tobias H. Colding and William P. Minicozzi II* 0. Introduction This paper is the second in a series where we give a description of the space of all embedded minimal surfaces of ﬁxed genus in a ﬁxed (but arbitrary) closed 3-manifold. The key for understanding such surfaces is to understand the local structure in a ball and in particular the structure of an embedded minimal disk in a ball in R3 . We show here that if the curvature of such a disk...

• ### Đề tài "Pseudodifferential operators on manifolds with a Lie structure at infinity "

We deﬁne and study an algebra Ψ∞ (M0 ) of pseudodiﬀerential opera1,0,V tors canonically associated to a noncompact, Riemannian manifold M0 whose geometry at inﬁnity is described by a Lie algebra of vector ﬁelds V on a compactiﬁcation M of M0 to a compact manifold with corners. We show that the basic properties of the usual algebra of pseudodiﬀerential operators on a compact manifold extend to Ψ∞ (M0 ).

• ### Research report: "The w - the germ of function defined on the manifold r-reticular"

Tham khảo luận văn - đề án 'research report: "the w - the germ of function defined on the manifold r-reticular"', luận văn - báo cáo phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả

• ### Báo cáo toán học: " Automated target tracking and recognition using coupled view and identity manifolds for shape representation"

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học được đăng trên tạp chí toán học quốc tế đề tài: Automated target tracking and recognition using coupled view and identity manifolds for shape representation

• ### Báo cáo hóa học: "Research Article A Metric Multidimensional Scaling-Based Nonlinear Manifold Learning Approach for Unsupervised Data Reduction"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article A Metric Multidimensional Scaling-Based Nonlinear Manifold Learning Approach for Unsupervised Data Reduction

• ### Đề tài " Positively curved manifolds with symmetry "

There are very few examples of Riemannian manifolds with positive sectional curvature known. In fact in dimensions above 24 all known examples are diﬀeomorphic to locally rank one symmetric spaces. We give a partial explanation of this phenomenon by showing that a positively curved, simply connected, compact manifold (M, g) is up to homotopy given by a rank one symmetric space, provided that its isometry group Iso(M, g) is large. More precisely we prove ﬁrst that if dim(Iso(M, g)) ≥ 2 dim(M ) − 6, then M is tangentially homotopically equivalent to a rank one symmetric space or M...

• ### Đề tài " Isometric actions of simple Lie groups on pseudoRiemannian manifolds "

Let M be a connected compact pseudoRiemannian manifold acted upon topologically transitively and isometrically by a connected noncompact simple Lie group G. If m0 , n0 are the dimensions of the maximal lightlike subspaces tangent to M and G, respectively, where G carries any bi-invariant metric, then we have n0 ≤ m0 . We study G-actions that satisfy the condition n0 = m0 .