共查询到20条相似文献,搜索用时 15 毫秒
1.
Themis Koufogiorgos 《Results in Mathematics》1995,27(1-2):51-62
In this paper we classify 3-dimensional complete contact Riemannian manifolds satisfying the following condition “the characteristic vector field is an eigenvector of the Ricci operator with constant eigenvalue”. Moreover we prove that this condition is equivalent with some other characteristic ones. 相似文献
2.
((Without abstract))
Submitted: December 1996, final version: June 1997 相似文献
3.
Optimal Configurations of Finite Sets in Riemannian 2-Manifolds 总被引:1,自引:0,他引:1
Peter M. Gruber 《Geometriae Dedicata》2001,84(1-3):271-320
4.
Shu-Cheng Chang 《Geometriae Dedicata》1997,64(3):253-260
In this article, we prove the compactness of the set of critical 4-manifolds with L
p-bound on the negative part of the Ricci curvature tensor, p > 2. In earlier work we proved this under the assumption that the Ricci curvature is pointwise bounded from below. 相似文献
5.
A well-known problem about Riemannian manifolds asks whether the isospectral manifolds are isometric. We settle this problem for compact flat 3-manifolds. 相似文献
6.
Bruno Zimmermann 《Monatshefte für Mathematik》2004,142(3):267-273
We consider the problem of whether a given hyperbolic surface occurs as the totally geodesic boundary of a compact hyperbolic 3-manifold (as some or as the only boundary component). We discuss some explicit examples of hyperbolic surfaces, in particular the surface associated to the small stellated dodecahedron (one of the four Kepler-Poinsot polyhedra) which is the boundary of a hyperbolic icosahedral 3-manifold. 相似文献
7.
Luis Ugarte 《Annals of Global Analysis and Geometry》2001,19(1):35-53
We introduce a differential complex of coeffective type for anySpin(7)-manifold M locally conformal to aRiemannian 8-manifold with holonomy contained in Spin(7).Local properties of this complex, such as ellipticity and acyclicity,are studied. The relationship between the coeffective cohomology ofM and the topology of the manifold is discussed in the caseof M having a subgroup of Spin(7) as aholonomy group. 相似文献
8.
Bruno Zimmermann 《Monatshefte für Mathematik》2004,134(1):267-273
We consider the problem of whether a given hyperbolic surface occurs as the totally geodesic boundary of a compact hyperbolic 3-manifold (as some or as the only boundary component). We discuss some explicit examples of hyperbolic surfaces, in particular the surface associated to the small stellated dodecahedron (one of the four Kepler-Poinsot polyhedra) which is the boundary of a hyperbolic icosahedral 3-manifold. 相似文献
9.
It is shown that a conformally flat contact metric 3-manifold with Ricci curvature vanishing along the characteristic vector field, has non-positive scalar curvature. Such a manifold is flat if (i) it is compact, or (ii) the scalar curvature is constant, or (iii) the norm of the Ricci tensor is constant. 相似文献
10.
Let M be a compact orientable irreducible 3-manifold, and F be an essential connected closed surface in M which cuts M into two manifolds M1 and M2. If Mi has a minimal Heegaard splitting Mi = Vi ∪Hi Wi with d(H1) + d(H2) ≥ 2(g(M1) + g(M2) -g(F)) + 1, then g(M) = g(M1) + g(M2) - g(F). 相似文献
11.
Ian Agol 《Geometriae Dedicata》2003,102(1):53-64
In this paper we prove the Cheeger inequality for infinite weighted graphs endowed with 'corresponding' measure. This measure has already been developed in the study of tree lattices. Our graphs have finite volumes. A similar theory has already been developed for manifolds of finite volumes. 相似文献
12.
In [2], H. Furstenberg studied a distal action of a locallycompact group G on a compact metric space X, and establisheda structure theorem. As a consequence, he showed that if G isabelian, then a simply connected space X does not admit a minimaldistal G-action. In this paper we concern ourselves with a nonsingular flow = {t} on a closed 3-manifold M. Recall that is called distalif for any distinct two points x, y M, the distance d(tx, ty)is bounded away from 0. The distality depends strongly uponthe time parametrization. For example, there exists a time parametrizationof a linear irrational flow on T2 which yields a nondistal flow[4, 6]. 1991 Mathematics Subject Classification 58F25, 57R30. 相似文献
13.
Bayram Ṣahin 《Acta Appl Math》2010,109(3):829-847
Riemannian maps were introduced by Fischer (Contemp. Math. 132:331–366, 1992) as a generalization isometric immersions and Riemannian submersions. He showed that such maps could be used to solve the
generalized eikonal equation and to build a quantum model. On the other hand, horizontally conformal maps were defined by
Fuglede (Ann. Inst. Fourier (Grenoble) 28:107–144, 1978) and Ishihara (J. Math. Kyoto Univ. 19:215–229, 1979) and these maps are useful for characterization of harmonic morphisms. Horizontally conformal maps (conformal maps) have
their applications in medical imaging (brain imaging)and computer graphics. In this paper, as a generalization of Riemannian
maps and horizontally conformal submersions, we introduce conformal Riemannian maps, present examples and characterizations.
We show that an application of conformal Riemannian maps can be made in weakening the horizontal conformal version of Hermann’s
theorem obtained by Okrut (Math. Notes 66(1):94–104, 1999). We also give a geometric characterization of harmonic conformal Riemannian maps and obtain decomposition theorems by using
the existence of conformal Riemannian maps. 相似文献
14.
15.
16.
Hong Huang 《Journal of Geometric Analysis》2013,23(3):1213-1235
In this note we prove the following result: Let X be a complete, connected 4-manifold with uniformly positive isotropic curvature, with bounded geometry, and with no essential incompressible space form. Then X is diffeomorphic to $\mathbb{S}^{4}$ , or $\mathbb{RP}^{4}$ , or $\mathbb{S}^{3}\times\mathbb {S}^{1}$ , or $\mathbb{S}^{3}\widetilde{\times} \mathbb{S}^{1}$ , or a possibly infinite connected sum of them. This extends work of Hamilton and Chen–Zhu to the noncompact case. The proof uses Ricci flow with surgery on complete 4-manifolds, and is inspired by recent work of Bessières, Besson, and Maillot. 相似文献
17.
On a compact Riemannian manifold,we prove a decomposition theorem for arbitrarily bounded energy sequence of solutions of a singular elliptic equation. 相似文献
18.
Joseph D. Masters 《Geometriae Dedicata》2006,119(1):17-33
We show that every closed, virtually fibered hyperbolic 3-manifold contains immersed, quasi-Fuchsian. 相似文献
19.
Gang Liu 《Inventiones Mathematicae》2013,193(2):367-375
For a complete noncompact 3-manifold with nonnegative Ricci curvature, we prove that either it is diffeomorphic to ?3 or the universal cover splits. This confirms Milnor’s conjecture in dimension 3. 相似文献
20.
Marc Lackenby 《Geometriae Dedicata》2004,109(1):139-145
Let M and M′ be simple 3-manifolds, each with connected boundary of genus at least two. Suppose that Mand M′ are glued via a homeomorphism between their boundaries. Then we show that, provided the gluing homeomorphism is ‘sufficiently complicated’, the Heegaard genus of the amalgamated manifold is completely determined by the Heegaard genus of Mand M′ and the genus of their common boundary. Here, a homeomorphism is ‘sufficiently complicated’ if it is the composition of a homeomorphism from the boundary ofM to some surface S, followed by a sufficiently high power of a pseudo-Anosov onS, followed by a homeomorphism to the boundary of M′. The proof uses the hyperbolic geometry of the amalgamated manifold, generalised Heegaard splittings and minimal surfaces. 相似文献