共查询到20条相似文献,搜索用时 15 毫秒
1.
Tudor Zamfirescu 《Geometriae Dedicata》1996,62(1):99-105
This paper discusses conjugate points on the geodesics of convex surfaces. It establishes their relationship with the cut locus. It shows the possibility of having many geodesics with conjugate points at very large distances from each other. It also shows that on many surfaces there are arbitrarily many closed geodesic arcs originating and ending at a common point. To achieve these goals, Baire category methods are employed. 相似文献
2.
We study the existence of simple closed geodesics on most (in the sense of Baire category) Alexandrov surfaces with curvature bounded below, compact and without boundary. We show that it depends on both the curvature bound and the topology of the surfaces. 相似文献
3.
4.
Jill McGowan 《Differential Geometry and its Applications》2005,22(1):81-104
Consider a compact, connected Lie group G acting isometrically on a sphere Sn of radius 1. The quotient of Sn by this group action, Sn/G, has a natural metric on it, and so we may ask what are its diameter and q-extents. These values have been computed for cohomogeneity one actions on spheres. In this paper, we compute the diameters, extents, and several q-extents of cohomogeneity two orbit spaces resulting from such actions, and we also obtain results about the q-extents of Euclidean disks. Additionally, via a simple geometric criterion, we can identify which of these actions give rise to a decomposition of the sphere as a union of disk bundles. In addition, as a service to the reader, we give a complete breakdown of all the isotropy subgroups resulting from cohomogeneity one and two actions. 相似文献
5.
F.Alberto Grünbaum 《Bulletin des Sciences Mathématiques》2003,127(3):207-214
For every value of the parameters α,β>−1 we find a matrix valued weight whose orthogonal polynomials satisfy an explicit differential equation of Jacobi type. 相似文献
6.
In this paper we give sufficient conditions for existence of error bounds for systems expressed in terms of eigenvalue functions
(such as in eigenvalue optimization) or positive semidefiniteness (such as in semidefinite programming).
The research of the author was partially supported by an NSERC grant. 相似文献
7.
Given a smooth compact Riemannian surface, we prove that if a suitable convexity assumption on the tangent focal cut loci is satisfied, then all injectivity domains are semiconvex. 相似文献
8.
Semi-Riemannian manifolds with a suitable set of conformal symmetries are shown to be complete. Locally warped products are studied and warped-completeness is introduced. In the case of definite and complete basis, several assumptions on the growth of the warping function yield some of the three kinds of completeness. The case of 1-dimensional basis (including a known family of relativistic space-times) is specially studied. Null warped-completeness is related to the completeness of a certain conformal metric on the basis. Several examples and counter-examples explaining the main results are also given.This work was supported in part by a DGICYT Grant PB91-0731 相似文献
9.
I. G. Nikolaev 《Commentarii Mathematici Helvetici》1995,70(1):210-234
Schur's theorem states that an isotropic Riemannian manifold of dimension greater than two has constant curvature. It is natural
to guess that compact almost isotropic Riemannian manifolds of dimension greater than two are close to spaces of almost constant
curvature. We take the curvature anisotropy as the discrepancy of the sectional curvatures at a point. The main result of
this paper is that Riemannian manifolds in Cheeger's class ℜ(n,d,V,A) withL
1-small integral anisotropy haveL
p-small change of the sectional curvature over the manifold. We also estimate the deviation of the metric tensor from that
of constant curvature in theW
p
2
-norm, and prove that compact almost isotropic spaces inherit the differential structure of a space form. These stability
results are based on the generalization of Schur' theorem to metric spaces. 相似文献
10.
11.
Michiko Tamura 《Journal of Geometry》1995,52(1-2):189-192
In the Euclidean 3-space, complete and connected smooth surfaces having two proper helical geodesics through each point are circular cylinders. 相似文献
12.
We study a 2-dimensional manifold that admits a homogeneous action of a 3-dimensional Lie group G, and has a 2-form invariant under G. We show that such a manifold can be realized as a surface in the affine 3-space, and list such realizations.
相似文献
13.
We consider three-dimensional unimodular Lie groups equipped with a Lorentzian metric and we determine, for all of them, their
sets of homogeneous geodesics through a point.
Dedicated to the memory of Professor Aldo Cossu
Authors supported by funds of M.U.R.S.T., G.N.S.A.G.A. and the University of Lecce. 相似文献
14.
For spacelike stationary (i.e. zero mean curvature) surfaces in 4-dimensional Lorentz space, one can naturally introduce two Gauss maps and a Weierstrass-type representation. In this paper we investigate the global geometry of such surfaces systematically. The total Gaussian curvature is related with the surface topology as well as the indices of the so-called good singular ends by a Gauss–Bonnet type formula. On the other hand, as shown by a family of counterexamples to Osserman?s theorem, finite total curvature no longer implies that Gauss maps extend to the ends. Interesting examples include the deformations of the classical catenoid, the helicoid, the Enneper surface, and Jorge–Meeks? k-noids. Each family of these generalizations includes embedded examples in the 4-dimensional Lorentz space, showing a sharp contrast with the 3-dimensional case. 相似文献
15.
We continue our study of the space of geodesics of a manifold with linear connection. We obtain sufficient conditions for a product to have a space of geodesics which is a manifold. We investigate the relationship of the space of geodesics of a covering manifold to that of the base space. We obtain sufficient conditions for a space to be geodesically connected in terms of the topology of its space of geodesics. 相似文献
16.
Each element $x$ of the commutator subgroup $[G, G]$ of a group $G$
can be represented as a product of commutators. The minimal number
of factors in such a product is called the commutator length of
$x$. The commutator length of $G$ is defined as the supremum of
commutator lengths of elements of $[G, G]$.
We show that for certain closed symplectic manifolds $(M,\omega)$,
including complex projective spaces and Grassmannians,
the universal cover $\widetilde{\hbox{\rm Ham}\, (M,\omega)$ of the group of Hamiltonian
symplectomorphisms of $(M,\omega)$ has infinite
commutator length. In particular, we present explicit examples of
elements in $\widetilde{\hbox{\rm Ham}\, (M,\omega)$ that have
arbitrarily large
commutator length -- the estimate on their commutator length
depends on the multiplicative structure of the quantum cohomology
of $(M,\omega)$. By a different method we also show that in the
case $c_1 (M) = 0$ the group
$\widetilde{\hbox{\rm Ham}\, (M,\omega)$ and the universal cover
${\widetilde{\Symp}}_0\, (M,\omega)$ of the identity
component of the group of symplectomorphisms of $(M,\omega)$
have infinite commutator length. 相似文献
17.
Huagui Duan Yiming Long 《Calculus of Variations and Partial Differential Equations》2008,31(4):483-496
We prove that for every Q-homological Finsler 3-sphere (M, F) with a bumpy and irreversible metric F, either there exist two non-hyperbolic prime closed geodesics, or there exist at least three prime closed geodesics.
Huagui Duan: Partially supported by NNSF and RFDP of MOE of China.
Yiming Long: Partially supported by the 973 Program of MOST, Yangzi River Professorship, NNSF, MCME, RFDP, LPMC of MOE of
China, S. S. Chern Foundation, and Nankai University. 相似文献
18.
This paper is concerned with realizations of the irreducible representations of the orthogonal group and construction of specific
bases for the representation spaces. As is well known, Weyl's branching theorem for the orthogonal group provides a labeling
for such bases, called Gelfand-Žetlin labels. However, it is a difficult problem to realize these representations in a way
that gives explicit orthogonal bases indexed by these Gelfand-–etlin labels. Thus, in this paper the irreducible representations
of the orthogonal group are realized in spaces of polynomial functions over the general linear groups and equipped with an
invariant differentiation inner product, and the Gelfand-Žetlin bases in these spaces are constructed explicitly. The algorithm
for computing these polynomial bases is illustrated by a number of examples.
Partially supported by a grant from the Department of Energy.
Partially supported by NSF grant No. MCS81-02345. 相似文献
19.
Dean Allison 《Geometriae Dedicata》1996,63(3):309-319
We investigate a class of semi-Riemannian submersions satisfying a Lorentzian analogue of the classical Clairaut's relation for surfaces of revolution. We show that a Lorentzian submersion with one-dimensional fibers is Clairaut if and only if the fibers are totally umbilic with a gradient field as the normal curvature vector field. We also investigate the behavior of timelike and null geodesics in Lorentzian Clairaut submersions. In particular, every null geodesic of a Lorentzian Clairaut submersion with one-dimensional fibers projects to a pregeodesic in the base space with respect to a conformally related metric on the base space if and only if the integrability tensor of the submersion vanishes. 相似文献
20.
The irreducible finite dimensional representations of the symplectic groups are realized as polynomials on the irreducible representation spaces of the corresponding general linear groups. It is shown that the number of times an irreducible representation of a maximal symplectic subgroup occurs in a given representation of a symplectic group, is related to the betweenness conditions of representations of the corresponding general linear groups. Using this relation, it is shown how to construct polynomial bases for the irreducible representation spaces of the symplectic groups in which the basis labels come from the representations of the symplectic subgroup chain, and the multiplicity labels come from representations of the odd dimensional general linear groups, as well as from subgroups. The irreducible representations of Sp(4) are worked out completely, and several examples from Sp(6) are given. 相似文献