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1.
By introducing an imaginary space transform curvature ρs, a complex space called Riemannian space is constructed, in which the light propagating in free space has the trajectory
of straight line while propagating. Moreover, this curvature couples with that of the wave front of the paraxial beam ρw, and therefore a complex curvature ρc is constructed, which can be employed to investigate the behavior of the light transmission and to generalize the ABCD law.
Project supported by the National Hi-Tech Inertial Confinement Fusion Committee, the Guangdong Natural Science Foundation
the Postdoctoral Foundation of Guangdong and National Postdoctoral Foundation of China. 相似文献
2.
61. IntroductionLet P be a submanifold of an n-dimensional riemannian manifold AI. Expressions fOrthe kth integrated mean curvatures, M^P(t), (i. e. the integral of tho kth mcan curvature,k = 0, 1,' l n -- l), of a tubular hypersurface P of radius t about P, in terms of theRiemann curvature tensor of P. are calculated when AI is Euclidean or a rank one symmetricspace[5'13"1. Moreover, when P is a closed convex hypersurface of thc n-dimensional spaceof constant curvature A', Santal6 has… 相似文献
3.
FANG FUQUAN 《数学年刊B辑(英文版)》2000,(4)
1. IntroductionBy [111, a hypersurface in a symmetric space is called equifocal if every normal geodesicperpendiculajr to it is closed of constant length, say l, and contains Zg focal points for somepositive integer g. This is a natural generalization of isoparametric hypersurfaces in sphereswhere the illteger g is the number of distinct principal curvatures. In this note we considerequifocal hypersurfaces in simply connected rank one symmetric spaces, i.e. the complexprojective space CP", th… 相似文献
4.
Uniqueness of complete spacelike hypersurfaces via their higher order mean curvatures in a conformally stationary spacetime
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Henrique Fernandes de Lima Marco Antonio Lázaro Velásquez 《Mathematische Nachrichten》2014,287(11-12):1223-1240
We study complete noncompact spacelike hypersurfaces immersed into conformally stationary spacetimes, that is, Lorentzian manifolds endowed with a timelike conformal vector field V. In this setting, by using as main analytical tool a suitable maximum principle for complete noncompact Riemannian manifolds, we establish new characterizations of totally umbilical hypersurfaces in terms of their higher order mean curvatures. For instance, supposing an appropriated restriction on the norm of the tangential component of the vector field V, we are able to show that such hypersurfaces must be totally umbilical provided that either some of their higher order mean curvatures are linearly related or one of them is constant. Applications to the so‐called generalized Robertson‐Walker spacetimes are given. In particular, we extend to the Lorentzian context a classical result due to Jellett 29 . 相似文献
5.
A. R. Veeravalli 《Commentarii Mathematici Helvetici》2001,76(1):155-160
For a closed hypersurface in a space form, this work provides some sharp upper bounds for its first positive Laplacian eigenvalue.
These bounds are extrinsic as they rely on the mean curvatures and center(s) of gravity of the hypersurface.
Received: May 22, 2000 相似文献
6.
Yu Fu 《Mathematische Nachrichten》2015,288(7):763-774
We obtain a complete classification of proper biharmonic hypersurfaces with at most three distinct principal curvatures in sphere spaces with arbitrary dimension. Precisely, together with known results of Balmu?‐Montaldo‐Oniciuc, we prove that compact orientable proper biharmonic hypersurfaces with at most three distinct principal curvatures in sphere spaces are either the hypersphere or the Clifford hypersurface with and . Moreover, we also show that there does not exist proper biharmonic hypersurface with at most three distinct principal curvatures in hyperbolic spaces . 相似文献
7.
We give a new proof of the generalized Minkowski identities relating the higher degree mean curvatures of orientable closed hypersurfaces immersed in a given constant sectional curvature manifold. Our methods rely on a fundamental differential system of Riemannian geometry introduced by the author. We develop the notion of position vector field, which lies at the core of the Minkowski identities. 相似文献
8.
Erwann Delay 《Advances in Mathematics》2002,168(2):213-224
On an asymptotically hyperbolic Einstein manifold (M,g0) for which the Yamabe invariant of the conformal structure on the boundary at infinity is nonnegative, we show that the operators of Ricci curvature, and of Einstein curvature, are locally invertible in a neighborhood of the metric g0. We deduce in the C∞ case that the image of the Riemann-Christoffel curvature operator is a submanifold in a neighborhood of g0. 相似文献
9.
Wenxiong Chen & Ruobing Zhang 《数学研究》2020,53(4):436-470
In this paper, we will explore the geometric effects of conformally covariant
operators and the induced nonlinear curvature equations in certain nonlocal nature.
Mainly, we will prove some regularity and rigidity results for the distributional solutions to those equations. 相似文献
10.
We prove anisotropic Reilly-type upper bounds for divergence-type operators on hypersurfaces of the Euclidean space in presence of a weighted measure. 相似文献