7,666 research outputs found
Degree-regular triangulations of the double-torus
A connected combinatorial 2-manifold is called degree-regular if each of its
vertices have the same degree. A connected combinatorial 2-manifold is called
weakly regular if it has a vertex-transitive automorphism group. Clearly, a
weakly regular combinatorial 2-manifold is degree-regular and a degree-regular
combinatorial 2-manifold of Euler characteristic - 2 must contain 12 vertices.
In 1982, McMullen et al. constructed a 12-vertex geometrically realized
triangulation of the double-torus in \RR^3. As an abstract simplicial
complex, this triangulation is a weakly regular combinatorial 2-manifold. In
1999, Lutz showed that there are exactly three weakly regular orientable
combinatorial 2-manifolds of Euler characteristic - 2. In this article, we
classify all the orientable degree-regular combinatorial 2-manifolds of Euler
characteristic - 2. There are exactly six such combinatorial 2-manifolds. This
classifies all the orientable equivelar polyhedral maps of Euler characteristic
- 2.Comment: 13 pages. To appear in `Forum Mathematicum
Direct optical excitation of a fullerene-incarcerated metal ion
The endohedral fullerene Er3N@C80 shows characteristic 1.5 micron
photoluminescence at cryogenic temperatures associated with radiative
relaxation from the crystal-field split Er3+ 4I13/2 manifold to the 4I15/2
manifold. Previous observations of this luminescence were carried out by
photoexcitation of the fullerene cage states leading to relaxation via the
ionic states. We present direct non-cage-mediated optical interaction with the
erbium ion. We have used this interaction to complete a
photoluminescence-excitation map of the Er3+ 4I13/2 manifold. This ability to
interact directly with the states of an incarcerated ion suggests the
possibility of coherently manipulating fullerene qubit states with light
Spaces of embeddings of compact polyhedra into 2-manifolds
Let M be a PL 2-manifold and X be a compact subpolyhedron of M and let E(X,
M) denote the space of embeddings of X into M with the compact-open topology.
In this paper we study an extension property of embeddings of X into M and show
that the restriction map from the homeomorphism group of M to E(X, M) is a
principal bundle. As an application we show that if M is a Euclidean PL
2-manifold and dim X >= 1 then the triple (E(X,M), E^LIP(X,M), E^PL(X, M)) is
an (s,Sigma,sigma)-manifold, where E_K^LIP(X,M) and E_K^PL(X, M) denote the
subspaces of Lipschitz and PL embeddings.Comment: 13 page
Plateau's problem with \v{C}ech homological conditions on manifold
Let be an -dimensional closed submanifold
of class , a positive integer between 1 and . We will solve
Plateau's problem of dimension on with \v{C}ech homology
conditions
Totally geodesic submanifolds in the tangent bundle of a Riemannian 2-manifold
We give a full description of totally geodesic submanifolds in the tangent
bundle of a Riemannian 2-manifold of constant curvature and present a new class
of a cylinder-type totally geodesic submanifolds in the general case.Comment: Matematicheskaya fizika, analiz, geometriya - to appea
Total excess and Tits metric for piecewise Riemannian 2-manifolds
AbstractA piecewise Riemannian 2-manifold is a combinatorial 2-manifold with a triangulation such that each 2-simplex is a geodesic triangle of some Riemannian 2-manifold. In this paper, we study the total excess e(X) of a simply connected nonpositively curved piecewise Riemannian 2-manifold X in connection with the Tits metric on the boundary at infinity X(∞)
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