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1.
Laguerre geometry of surfaces in is given in the book of Blaschke [Vorlesungen über Differentialgeometrie, Springer, Berlin Heidelberg New York (1929)], and has been studied by Musso and Nicolodi [Trans. Am. Math. soc. 348, 4321–4337 (1996); Abh. Math. Sem. Univ. Hamburg 69, 123–138 (1999); Int. J. Math. 11(7), 911–924 (2000)], Palmer [Remarks on a variation problem in Laguerre geometry. Rendiconti di Mathematica, Serie VII, Roma, vol. 19, pp. 281–293 (1999)] and other authors. In this paper we study Laguerre differential geometry of hypersurfaces in . For any umbilical free hypersurface with non-zero principal curvatures we define a Laguerre invariant metric g on M and a Laguerre invariant self-adjoint operator : TM → TM, and show that is a complete Laguerre invariant system for hypersurfaces in with n≥ 4. We calculate the Euler–Lagrange equation for the Laguerre volume functional of Laguerre metric by using Laguerre invariants. Using the Euclidean space , the semi-Euclidean space and the degenerate space we define three Laguerre space forms , and and define the Laguerre embeddings and , analogously to what happens in the Moebius geometry where we have Moebius space forms S
n
, and (spaces of constant curvature) and conformal embeddings and [cf. Liu et al. in Tohoku Math. J. 53, 553–569 (2001) and Wang in Manuscr. Math. 96, 517–534 (1998)]. Using these Laguerre embeddings we can unify the Laguerre geometry of hypersurfaces in , and . As an example we show that minimal surfaces in or are Laguerre minimal in .C. Wang Partially supported by RFDP and Chuang-Xin-Qun-Ti of NSFC. 相似文献
2.
Thomas Westerbäck 《Designs, Codes and Cryptography》2007,42(3):335-355
A maximal partial Hamming packing of is a family of mutually disjoint translates of Hamming codes of length n, such that any translate of any Hamming code of length n intersects at least one of the translates of Hamming codes in . The number of translates of Hamming codes in is the packing number, and a partial Hamming packing is strictly partial if the family does not constitute a partition of .
A simple and useful condition describing when two translates of Hamming codes are disjoint or not disjoint is proved. This
condition depends on the dual codes of the corresponding Hamming codes. Partly, by using this condition, it is shown that
the packing number p, for any maximal strictly partial Hamming packing of , n = 2
m
−1, satisfies .
It is also proved that for any n equal to 2
m
−1, , there exist maximal strictly partial Hamming packings of with packing numbers n−10,n−9,n−8,...,n−1. This implies that the upper bound is tight for any n = 2
m
−1, .
All packing numbers for maximal strictly partial Hamming packings of , n = 7 and 15, are found by a computer search. In the case n = 7 the packing number is 5, and in the case n = 15 the possible packing numbers are 5,6,7,...,13 and 14.
相似文献
3.
In this article we extend Milnor’s fibration theorem to the case of functions of the form with f, g holomorphic, defined on a complex analytic (possibly singular) germ (X, 0). We further refine this fibration theorem by looking not only at the link of , but also at its multi-link structure, which is more subtle. We mostly focus on the case when X has complex dimension two. Our main result (Theorem 4.4) gives in this case the equivalence of the following three statements:
Moreover one has that if these conditions hold, then the Milnor-Lê fibration of is a fibration of the multilink . We also give a combinatorial criterium to decide whether or not the multilink is fibered. If the meromorphic germ f/g is semitame, then we show that the Milnor-Lê fibration given by is equivalent to the usual Milnor fibration given by . We finish this article by discussing several realization problems.
Research partially supported by CONACYT and DGAPA-UNAM, Mexico, and by CNRS and ECOS, France. 相似文献
(i) | The real analytic germ has 0 as an isolated critical value; |
(ii) | the multilink is fibered; and |
(iii) | if is a resolution of the holomorphic germ , then for each rupture vertex (j) of the decorated dual graph of π one has that the corresponding multiplicities of f, g satisfy: . |
4.
In this paper we fix a set * of positive elements of the free group
(e. g. the set of finite words occurring in a Markov subshift) as well as n partial isometries on a Hilbert space H. Based on these we define a map S :
which we prove to be a partial representation of
on H under certain conditions studied by Matsumoto.*Supported by Capes. 相似文献
5.
Andrew Raich 《Mathematische Zeitschrift》2007,256(1):193-220
Let be a subharmonic, nonharmonic polynomial and a parameter. Define , a closed, densely defined operator on . If and , we solve the heat equations , u(0,z) = f(z) and , . We write the solutions via heat semigroups and show that the solutions can be written as integrals against distributional
kernels. We prove that the kernels are C
∞ off of the diagonal {(s, z, w) : s = 0 and z = w} and find pointwise bounds for the kernels and their derivatives.
相似文献
6.
Let be a C
2 map and let Spec(Y) denote the set of eigenvalues of the derivative DY
p
, when p varies in . We begin proving that if, for some ϵ > 0, then the foliation with made up by the level surfaces {k = constant}, consists just of planes. As a consequence, we prove a bijectivity result related to the three-dimensional case
of Jelonek’s Jacobian Conjecture for polynomial maps of
The first author was supported by CNPq-Brazil Grant 306992/2003-5. The first and second author were supported by FAPESP-Brazil
Grant 03/03107-9. 相似文献
7.
Summary.
Let
We say that
preserves the distance d 0 if
for each
implies
Let A
n
denote the set of all positive numbers
d such that any map
that preserves unit distance preserves also distance
d.
Let D
n
denote the set of all positive numbers
d with the property: if
and
then there exists a finite set
S
xy
with
such that any map
that preserves unit distance preserves also the distance between
x and y.
Obviously,
We prove:
(1)
(2)
for n 2
D
n
is a
dense subset of
(2) implies that each mapping
f
from
to
(n 2)
preserving unit distance preserves all distances,
if f is continuous with respect to the product topologies
on
and
相似文献
8.
J. Bourgain 《Israel Journal of Mathematics》2009,172(1):61-74
Distributional properties of small multiplicative subgroups of are obtained. In particular, it is shown that if H < is of size larger than polylogarithmic in p, then, letting β < 1 be a fixed exponent, most elements of any coset aH (a ∈ , arbitrary) will not fall into the interval [−p
β, p
β] ∈ . The arguments are based on the theory of heights and results from additive combinatoric. 相似文献
9.
Claudemir Aniz 《Central European Journal of Mathematics》2008,6(4):497-503
Let K be a CW-complex of dimension 3 such that H
3(K;ℤ) = 0 and the orbit space of the 3-sphere with respect to the action of the quaternion group Q
8 determined by the inclusion Q
8 ⊆ . Given a point a ∈ , we show that there is no map f:K → which is strongly surjective, i.e., such that MR[f,a]=min{#(g
−1(a))|g ∈ [f]} ≠ 0.
相似文献
10.
P. Habegger 《Mathematische Annalen》2008,342(2):449-466
Let be an irreducible closed subvariety defined over . We bound the height of algebraic points on X that are in a certain sense close to the union of all algebraic subgroup of of dimension m < n/dim X. The bound we obtain is effective and will be expressed as a function of the height of X, the degree of X, and n. We then apply this bound to derive certain finiteness results if m is also strictly less than n − dim X. 相似文献
11.
Using the methods of moving frames and exterior differential systems, we show that there exist Hopf hypersurfaces in complex
hyperbolic space with any specified value of the Hopf principal curvature α less than or equal to the corresponding value for the horosphere. We give a construction for all such hypersurfaces in terms
of Weierstrass-type data, and also obtain a classification of pseudo-Einstein hypersurfaces in .
相似文献
12.
We give an explicit construction of any simply connected superconformal surface in Euclidean space in terms of a pair of conjugate minimal surfaces . That is superconformal means that its ellipse of curvature is a circle at any point. We characterize the pairs (g, h) of conjugate minimal surfaces that give rise to images of holomorphic curves by an inversion in and to images of superminimal surfaces in either a sphere or a hyperbolic space by an stereographic projection. We also determine the relation between the pairs (g, h) of conjugate minimal surfaces associated to a superconformal surface and its image by an inversion. In particular, this
yields a new transformation for minimal surfaces in . 相似文献
13.
We generalize the concept of K-convexity to an n-dimensional Euclidean space. The resulting concept of
-convexity is useful in addressing production and inventory problems where there are individual product setup costs and/or
joint setup costs. We derive some basic properties of
-convex functions. We conclude the paper with some suggestions for future research.
Support from Columbia University and University of Texas at Dallas is gratefully acknowledged. Helpful comments from Qi Feng
are appreciated. 相似文献
14.
The sharp lower bound for the volume of threefolds of general type with $${\chi({\mathcal O}_X)=1}$$
Lei Zhu 《Mathematische Zeitschrift》2009,261(1):123-141
Let V be a smooth projective threefold of general type. Denote by K
3, a rational number, the self-intersection of the canonical sheaf of any minimal model of V. One defines K
3 as a canonical volume of V. The paper is devoted to proving the sharp lower bound which can be reached by an example: .
Lei Zhu was supported by Fudan Graduate Students’ Innovation Projects (EYH5928004). 相似文献
15.
E. H. El Kinani 《Advances in Applied Clifford Algebras》2003,13(2):127-131
In this paper we construct the quantum Virasoro algebra
generators in terms of operators of the generalized Clifford algebras Cnk. Precisely, we show that
can be embedded into generalized Clifford algebras.
Junior Associate at The Abdus Salam ICTP, Trieste, Italy. 相似文献
16.
Kenley Jung 《Mathematische Annalen》2007,338(1):241-248
Suppose M is a tracial von Neumann algebra embeddable into (the ultraproduct of the hyperfinite II1-factor) and X is an n-tuple of selfadjoint generators for M. Denote by Γ(X; m, k, γ) the microstate space of X of order (m, k ,γ). We say that X is tubular if for any ε > 0 there exist and γ > 0 such that if then there exists a k × k unitary u satisfying for each 1 ≤ i ≤ n. We show that the following conditions are equivalent:
Research supported in part by the NSF.
Dedicated to Ed Effros on the occasion of his 70th birthday. 相似文献
• | M is amenable (i.e., injective). |
• | X is tubular. |
• | Any two embeddings of M into are conjugate by a unitary . |
17.
We prove that any simply connected
-manifold of CR-codimension s 2 is noncompact by showing that the
complete, simply connected
-manifolds are all the CR products N × {s-1} with N Sasakian, endowed with a
suitable product metric. N is a Sasakian -symmetric space if and only if M is CR-symmetric. The locally CR-symmetric
-manifolds are characterized by
=0 where
is the Tanaka--Webster connection. This characterization is showed to be nonvalid for nonnormal almost
-manifolds.Mathematics Subject Classifications (2000). 53C25, 53C35, 32V05. 相似文献
18.
Xiu Gui LIU 《数学学报(英文版)》2007,23(6):1025-1032
Abstract Let A be the mod p Steenrod algebra and S the sphere spectrum localized at p, where p is an odd prime. In 2001 Lin detected a new family in the stable homotopy of spheres which is represented by (b0hn-h1bn-1)∈ ExtA^3,(p^n+p)q(Zp,Zp) in the Adams spectral sequence. At the same time, he proved that i.(hlhn) ∈ExtA^2,(p^n+P)q(H^*M, Zp) is a permanent cycle in the Adams spectral sequence and converges to a nontrivial element ξn∈π(p^n+p)q-2M. In this paper, with Lin's results, we make use of the Adams spectral sequence and the May spectral sequence to detect a new nontrivial family of homotopy elements jj′j^-γsi^-i′ξn in the stable homotopy groups of spheres. The new one is of degree p^nq + sp^2q + spq + (s - 2)q + s - 6 and is represented up to a nonzero scalar by hlhnγ-s in the E2^s+2,*-term of the Adams spectral sequence, where p ≥ 7, q = 2(p - 1), n ≥ 4 and 3 ≤ s 〈 p. 相似文献
19.
In this paper, we characterize the dynamic of every Abelian subgroups
of
,
or
. We show that there exists a
-invariant, dense open set U in
saturated by minimal orbits with
a union of at most n
-invariant vector subspaces of
of dimension n−1 or n−2 over
. As a consequence,
has height at most n and in particular it admits a minimal set in
.
This work is supported by the research unit: systèmes dynamiques et combinatoire: 99UR15-15 相似文献
20.
We prove that every [n, k, d]
q
code with q ≥ 4, k ≥ 3, whose weights are congruent to 0, −1 or −2 modulo q and is extendable unless its diversity is for odd q, where .
相似文献