共查询到20条相似文献,搜索用时 31 毫秒
1.
Vincent Grandjean 《Bulletin of the Brazilian Mathematical Society》2008,39(4):515-535
Given a definable function f: ℝ
n
↦ ℝ, enough differentiable, we study the continuity of the total curvature function t → K(t), total curvature of the level f
−1(t), and the total absolute curvature function t → |K|(t), total absolute curvature of the level f
−1(t). We show they admits at most finitely many discontinuities.
Partially supported by the European research network IHP-RAAG contract number HPRN-CT-2001-00271 and partially supported by
Deutsche Forschungs-Gemeinschaft in the Priority Program Global Differential Geometry. 相似文献
2.
Recent results using inverse scattering techniques interpret every solution φ(x, y) of the sine-Gordon equation as a nonlinear superposition of solutions along the axes x=0 and y=0. This has a well-known geometric interpretation, namely that every weakly regular surface of Gauss curvature K=−1, in arc length asymptotic line parametrization, is uniquely determined by the values φ(x, 0) and φ(0, y) of its coordinate angle along the axes. We introduce a generalized Weierstrass representation of pseudospherical surfaces that depends only on these values, and we explicitely construct the associated family of pseudospherical immersions corresponding to it.Mathematics Subject Classifications (2000): 53A10, 58E20. 相似文献
3.
Rolf Schneider 《Annali di Matematica Pura ed Applicata》1978,116(1):101-134
Summary The curvature measures, introduced by Federer for the sets of positive reach, are investigated in the special case of convex
bodies. This restriction yields additional results. Among them are:(5.1), an integral-geometric interpretation of the curvature measure of order m, showing that it measures, in a certain sense,
the affine subspaces of codimension m+1 which touch the convex body;(6.1), an axiomatic characterization of the (linear combinations of) curvature measures similar to Hadwiger's characterization
of the quermassintegrals of convex bodies;(8.1), the determination of the support of the curvature measure of order m, which turns out to be the closure of the m-skeleton
of the convex body. Moreover we give, for the case of convex bodies, a new and comparatively short proof of an integral-geometric
kinematic formula for curvature measures.
Entrata in Redazione il 14 dicembre 1976. 相似文献
4.
We consider a C
1 smooth surface with prescribed p (or H)-mean curvature in the 3-dimensional Heisenberg group. Assuming only the prescribed p-mean curvature we show that any characteristic curve is C
2 smooth and its (line) curvature equals − H in the nonsingular domain. By introducing characteristic coordinates and invoking the jump formulas along characteristic
curves, we can prove that the Legendrian (or horizontal) normal gains one more derivative. Therefore the seed curves are C
2 smooth. We also obtain the uniqueness of characteristic and seed curves passing through a common point under some mild conditions,
respectively. These results can be applied to more general situations. 相似文献
5.
This paper gives a classification of complete hypersurfaces with nonzero constant mean curvature and constant quasi-Gauss-Kronecker curvature in the hyperbolic space H4(-1),whose scalar curvature is bounded from below. 相似文献
6.
Yu. A. Aminov 《Journal of Mathematical Sciences》1994,72(4):3155-3159
It is assumed that a domain of a three-dimensional Lobachevsky space with curvature equal to – 1 is immersed into E
5.It is known that four asymptotic lines pass through every point on the immersed domain. It is proved that the second curvature of the asymptotic line is k
2 =1/cos, where is the angle formed by vector 3
from the natural frame of the asymptotic line and the normal plane of the submanifold. The third curvature k
3
satisfies k
3 |(d/ds) (1/k
2
) |and if k
3
0, then the fourth curvature is expressed in terms of k
2
and k
3.Thus, any curve in E
5
may not be an asymptotic line on a domain of a Lobachevsky space immersed in E
5.Translated from Ukrainskii Geometricheskii Sbornik, No. 35, pp. 5–10, 1992. 相似文献
7.
J. I. Abdullaev 《Theoretical and Mathematical Physics》2006,147(1):486-495
We consider the Hamiltonian of a system of two fermions on a one-dimensional integer lattice. We prove that the number of
bound states N(k) is a nondecreasing function of the total quasimomentum of the system k ∈ [0, π]. We describe the set of discontinuity points of N(k) and evaluate the jump N(k +0) − N(k) at the discontinuity points. We establish that the bound-state energy z
n
(k) increases as the total quasimomentum k ∈ [0, π] increases.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 1, pp. 47–57, April, 2006. 相似文献
8.
Some Aspects on the Geometry of the Tangent Bundles and Tangent Sphere Bundles of a Riemannian Manifold 总被引:1,自引:0,他引:1
Marian Ioan Munteanu 《Mediterranean Journal of Mathematics》2008,5(1):43-59
In this paper we study a Riemannian metric on the tangent bundle T(M) of a Riemannian manifold M which generalizes Sasaki metric and Cheeger–Gromoll metric and a compatible almost complex structure which confers a structure
of locally conformal almost K?hlerian manifold to T(M) together with the metric. This is the natural generalization of the well known almost K?hlerian structure on T(M). We found conditions under which T(M) is almost K?hlerian, locally conformal K?hlerian or K?hlerian or when T(M) has constant sectional curvature or constant scalar curvature. Then we will restrict to the unit tangent bundle and we find
an isometry with the tangent sphere bundle (not necessary unitary) endowed with the restriction of the Sasaki metric from
T(M). Moreover, we found that this map preserves also the natural contact structures obtained from the almost Hermitian ambient
structures on the unit tangent bundle and the tangent sphere bundle, respectively.
This work was also partially supported by Grant CEEX 5883/2006–2008, ANCS, Romania. 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.
N. Blažić M. Prvanović 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2001,71(1):35-47
Let(M, g, J) be an almost Hermitian manifold. In this paper we study holomorphically nonnegatively(δ,Δ)-pinched almost Hermitian manifolds. In [3] it was shown that for such Kahler manifolds a plane with maximal sectional curvature
has to be a holomorphic plane(J-invariant). Here we generalize this result to arbitrary almost Hermitian manifolds with respect to the holomorphic curvature
tensorH R and toRK-manifolds of a constant type λ(p). In the proof some estimates of the sectional curvature are established. The results obtained are used to characterize almost
Hermitian manifolds of constant holomorphic sectional curvature (with respect to holomorphic and Riemannian curvature tensor)
in terms of the eigenvalues of the Jacobi-type operators, i.e. to establish partial cases of the Osserman conjecture. Some
examples are studied.
The first author is partially supported by SFS, Project #04M03. 相似文献
11.
We derive the integral inequality of a Randers metric with isotropic S-curvature in terms of its navigation representation. Using the obtained inequality we give some rigidity results under the condition of Ricci curvature. In particular, we show the following result: Assume that an n-dimensional compact Randers manifold (M, F) has constant S-curvature c. Then (M, F) must be Riemannian if its Ricci curvature satisfies that Ric 〈 -(n - 1)c^2. 相似文献
12.
In this paper we prove that a compact oriented hypersurface of a Euclidean
sphere with nonnegative Ricci curvature and infinite fundamental group is isometric
to an H(r)-torus
with constant mean curvature. Furthermore, we generalize, whithout any
hypothesis about the mean curvature, a characterization of Clifford torus due to
Hasanis and Vlachos.
Received: 19 March 2002 相似文献
13.
Spacelike hypersurfaces with constant scalar curvature 总被引:1,自引:0,他引:1
In this paper, we shall give an integral equality by applying the operator □ introduced by S.Y. Cheng and S.T. Yau [7] to
compact spacelike hypersurfaces which are immersed in de Sitter space S
n
+1
1(c) and have constant scalar curvature. By making use of this integral equality, we show that such a hypersurface with constant
scalar curvature n(n-1)r is isometric to a sphere if r << c.
Received: 18 December 1996 / Revised version: 26 November 1997 相似文献
14.
Ezequiel R. Barbosa Marcos Montenegro 《Bulletin of the Brazilian Mathematical Society》2008,39(3):427-445
In this work we present some properties satisfied by the second L
2-Riemannian Sobolev best constant along the Ricci flow on compact manifolds of dimensions n ≥ 4. We prove that, along the Ricci flow g(t), the second best constant B
0(2, g(t)) depends continuously on t and blows-up in finite time. In certain cases, the speed of the explosion is, at least, the same one of the curvature operator.
We also show that, on manifolds with positive curvature operator or pointwise 1/4-pinched curvature, one of the situations
holds: B
0(2, g(t)) converges to an explicit constant or extremal functions there exists for t large.
相似文献
15.
In this paper, we classify complete spacelike hypersurfaces in the anti-de Sitter space (n?3) with constant scalar curvature and with two principal curvatures. Moreover, we prove that if Mn is a complete spacelike hypersurface with constant scalar curvature n(n−1)R and with two distinct principal curvatures such that the multiplicity of one of the principal curvatures is n−1, then R<(n−2)c/n. Additionally, we also obtain several rigidity theorems for such hypersurfaces. 相似文献
16.
The problem of the diffraction of creeping waves on a point of transition of the convex boundary to the straight boundary
of a domain is investigated. It is assumed that at the point of jump of curvature, the tangent to the boundary is continuous
and its derivative has a jump. An expression for the edge wave is obtained and investigated. Bibliography: 4 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 250, 1998, pp. 274–287.
Translated by N. Ya. Kirpichnikova. 相似文献
17.
P. V. Svetlov 《Journal of Mathematical Sciences》2004,119(1):112-116
The conditions under which an infinite three-dimensional graph manifold M carries a metric of nonpositive bounded curvature (an NPC-metric) having finite volume are studied. A complete list of all such manifolds is obtained in the case where M is the mapping torus of a collection of Dehn twists on a surface of infinite genus and the graph of M is linear (i.e., homeomorphic to a line or a ray). Bibliography: 4 titles. 相似文献
18.
Chengbo Yue 《Israel Journal of Mathematics》1997,97(1):113-123
We answer a question of Gromov ([G2]) in the codimension 1 case: ifF is a codimension 1 foliation of a compact manifoldM with leaves of negative curvature, thenπ
1(M) has exponential growth. We also prove a result analogous to Zimmer’s ([Z2]): ifF is a codimension 1 foliation on a compact manifold with leaves of nonpositive curvature, and ifπ
1(M) has subexponential growth, then almost every leaf is flat. We give a foliated version of the Hopf theorem on surfaces without
conjugate points.
Partially supported by NSF Grant #DMS 9403870. 相似文献
19.
XuYINFENG 《高校应用数学学报(英文版)》1996,11(2):235-238
Abstract. Let S be a set of finite plauar points. A llne segment L(p, q) with p, q E Sis called a stable line segment of S, if there is no Line segment with two endpoints in S intersecting L(p, q). In this paper, some geometric properties of the set of all stable line segments 相似文献
20.
Assume that a submanifold M ? ?n of an arbitrary codimension k ? {1, …, n} is closed in some open set O→?n. With a given function u ? C2(O\M) we may associate its trivial extension u: O→? such that u|O\M=u and u|m ≡ 0. The jump of the Laplacian of the function u on the submanifold M is defined by the distribution Δu — Δu. By applying some general version of the Fubini theorem to the nonlinear projection onto M we obtain the formula for the jump of the Laplacian (Theorem 2.2). 相似文献