共查询到20条相似文献,搜索用时 15 毫秒
1.
The classical Three Gap Theorem asserts that for a natural number n and a real number p, there are at most three distinct distances between consecutive elements in the subset of [0,1) consisting of the reductions
modulo 1 of the first n multiples of p. Regarding it as a statement about rotations of the circle, we find results in a similar spirit pertaining to isometries
of compact Riemannian manifolds and the distribution of points along their geodesics.
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2.
Jesús A. Álvarez López Yuri A. Kordyukov Eric Leichtnam 《Mathematische Nachrichten》2014,287(14-15):1589-1608
Continuing the study of bounded geometry for Riemannian foliations, begun by Sanguiao, we introduce a chart‐free definition of this concept. Our main theorem states that it is equivalent to a condition involving certain normal foliation charts. For this type of charts, it is also shown that the derivatives of the changes of coordinates are uniformly bounded, and there are nice partitions of unity. Applications to a trace formula for foliated flows will be given in a forthcoming paper. 相似文献
3.
Howard E. Brandt 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(12):e474
A review is given of some recent developments in the differential geometry of quantum computation for which the quantum evolution is described by the special unitary unimodular group, SU(2n). Using the Lie algebra su(2n), detailed derivations are given of a useful Riemannian geometry of SU(2n), including the connection and the geodesic equation for minimal complexity quantum computations. 相似文献
4.
Mohamed Boucetta 《Journal of the Egyptian Mathematical Society》2011,19(1-2):57-70
We introduce Riemannian Lie algebroids as a generalization of Riemannian manifolds and we show that most of the classical tools and results known in Riemannian geometry can be stated in this setting. We give also some new results on the integrability of Riemannian Lie algebroids. 相似文献
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Simon Brendle 《Japanese Journal of Mathematics》2011,6(1):45-61
A fundamental question in Riemannian geometry is to find canonical metrics on a given smooth manifold. In the 1980s, R.S.
Hamilton proposed an approach to this question based on parabolic partial differential equations. The goal is to start from
a given initial metric and deform it to a canonical metric by means of an evolution equation. There are various natural evolution
equations for Riemannian metrics, including the Ricci flow and the conformal Yamabe flow. In this survey, we discuss the global
behavior of the solutions to these equations. In particular, we describe how these techniques can be used to prove the Differentiable
Sphere Theorem. 相似文献
8.
Aris Daniilidis Robert Deville Estibalitz Durand-Cartagena Ludovic Rifford 《Journal of Mathematical Analysis and Applications》2018,457(2):1333-1352
It is established that every self-contracted curve in a Riemannian manifold has finite length, provided its image is contained in a compact set. 相似文献
9.
Seiki Nhikawa Philippe Tondeur Lieven Vanhecke 《Annals of Global Analysis and Geometry》1992,10(3):291-304
Let F be a Riemannian foliation on a Riemannian manifold (M, g), with bundle-like metric g. Aside from the Laplacian △g associated to the metric g, there is another differential operator, the Jacobi operator J▽, which is a second order elliptic operator acting on sections of the normal bundle. Its spectrum is discrete as a consequence of the compactness of M. Hence one has two spectra, spec (M, g) = spectrum of △g (acting on functions), and spec (F, J▽) = spectrum of J▽. We discuss the following problem: Which geometric properties of a Riemannian foliation F on a Riemannian manifold (M, g) are determined by the two types of spectral invariants? 相似文献
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S. V. Buyalo 《Mathematical Notes》1976,19(5):468-473
An exact upper estimate for the volume of a tubular neighborhood of a smooth submanifold N of a complete Riemann space M depending upon the volume of N and lower bound for the sectional curvatures of M is given. If N is a closed geodesic, then the equality is attained in the estimate if and only if M is a generalized lens space.Translated from Matematicheskie Zametki, Vol. 19, No. 5, pp. 795–804, May, 1976.The author thanks Yu. D. Burago for help and guidance. 相似文献
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André Diatta 《Geometriae Dedicata》2008,133(1):83-94
We investigate contact Lie groups having a left invariant Riemannian or pseudo-Riemannian metric with specific properties
such as being bi-invariant, flat, negatively curved, Einstein, etc. We classify some of such contact Lie groups and derive
some obstruction results to the existence of left invariant contact structures on Lie groups.
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16.
We give manifolds whose Riemann curvature operators commute, i.e. which satisfy
for all tangent vectors xi in both the Riemannian and the higher signature settings. These manifolds have global geometric phenomena which are quite
different for higher signature manifolds than they are for Riemannian manifolds. Our focus is on global properties; questions
of geodesic completeness and the behaviour of the exponential map are investigated.
Dedicated to the memory of Jean Leray 相似文献
17.
Shen Yibing 《数学学报(英文版)》1996,12(3):298-313
This paper deals with superminimal surfaces in complex space forms by using the Frenet framing. We formulate explicitly the length squares of the higher fundamental forms and the higher curvatures for superminimal surfaces in terms of the metric of the surface and the Khler angle of the immersion. Particularly, some curvature pinching theorems for minimal 2-spheres in a complex projective space are given and a new characterization of the Veronese sequence is obtained.Supported by the National Natural Science Fundation of China. 相似文献
18.
A. Caminha 《Bulletin of the Brazilian Mathematical Society》2011,42(2):277-300
In this paper we examine different aspects of the geometry of closed conformal vector fields on Riemannian manifolds. We begin
by getting obstructions to the existence of closed conformal and nonparallel vector fields on complete manifolds with nonpositive
Ricci curvature, thus generalizing a theorem of T.K. Pan. Then we explain why it is so difficult to find examples, other than
trivial ones, of spaces having at least two closed, conformal and homothetic vector fields. We then focus on isometric immersions,
firstly generalizing a theorem of J. Simons on cones with parallel mean curvature to spaces furnished with a closed, Ricci
null conformal vector field; then we prove general Bernstein-type theorems for certain complete, not necessarily cmc, hypersurfaces
of Riemannian manifolds furnished with closed conformal vector fields. In particular, we obtain a generalization of theorems
J. Jellett and A. Barros and P. Sousa for complete cmc radial graphs over finitely punctured geodesic spheres of Riemannian
space forms. 相似文献
19.
In this paper, similarity symplectic geometry for curves is proposed and studied. Explicit expressions of the symplectic invariants, Frenet frame and Frenet formulae for curves in similarity symplectic geometry are obtained by using the equivariant moving frame method. The relationships between the Euclidean symplectic invariants, Frenet frame, Frenet formulae and the similarity symplectic invariants, Frenet frame, Frenet formulae for curves are established. Invariant curve flows in four-dimensional similarity symplectic geometry are also studied. It is shown that certain intrinsic invariant curve flows in four-dimensional similarity symplectic geometry are related to the integrable Burgers and matrix Burgers equations. 相似文献
20.
Esteban Andruchow 《Differential Geometry and its Applications》2005,23(3):305-326
A riemannian metric is introduced in the infinite dimensional manifold Σn of positive operators with rank n<∞ on a Hilbert space H. The geometry of this manifold is studied and related to the geometry of the submanifolds Σp of positive operators with range equal to the range of a projection p (rank of p=n), and Pp of selfadjoint projections in the connected component of p. It is shown that these spaces are complete in the geodesic distance. 相似文献