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1.
Consider oriented surfaces immersed in
. Associated to them,
here are studied pairs of transversal foliations with
singularities, defined on the Elliptic region, where the
Gaussian curvature
, given
by the product of the principal curvatures
k
1,
k
2 is
positive. The leaves of the foliations are the
lines of harmonic mean
curvature, also called characteristic or
diagonal lines, along which
the normal curvature of the immersion is given by
, where
is the
arithmetic mean curvature. That is,
is the harmonic mean of the
principal curvatures k
1,
k
2 of
the immersion. The singularities of the foliations are the
umbilic points and
parabolic curves, where
k
1 =
k
2 and
, respectively.Here are determined the structurally stable patterns of
harmonic mean curvature lines
near the umbilic points, parabolic
curves and harmonic mean
curvature cycles, the periodic leaves of the
foliations. The genericity of these patterns is
established.This provides the three essential local ingredients to
establish sufficient conditions, likely to be also necessary,
for Harmonic Mean Curvature Structural
Stability of immersed surfaces. This study, outlined
towards the end of the paper, is a natural analog and complement
for that carried out previously by the authors for the
Arithmetic Mean Curvature and
the Asymptotic Structural
Stability of immersed surfaces, [13, 14, 17], and
also extended recently to the case of the
Geometric Mean Curvature
Configuration [15].The first author was partially supported by FUNAPE/UFG.
Both authors are fellows of CNPq.
This work was done under the project PRONEX/FINEP/MCT -
Conv. 76.97.1080.00 - Teoria Qualitativa das Equações Diferenciais
Ordinárias and CNPq - Grant 476886/2001-5. 相似文献
2.
Amnon Neeman 《K-Theory》2001,22(1-2):1-144
Let
be a triangulated category, and assume it admits at least one model. In this article, we define a K-theory for
. The main theorem is that, given any bounded i-structure on
, the K-theory of the heart agrees with the K-theory of
. An immediate consequence tells us that, if two Abelian categories occur as hearts of a triangulated category for two different t-structures, then their K-theories must be isomorphic.The proof was also sketched in previous articles in this series. The virtue of this article is in the careful detail in which it is written down. 相似文献
3.
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.
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
6.
Violeta Petkova 《Archiv der Mathematik》2005,84(4):311-324
Let
be a weighted space with weight . In this paper we show that for every Wiener-Hopf operator T on
and for every a I, there exists a function
such that
for all
Here (g)a denotes the function x g(x)eax for
and
where R+ is the spectral radius of the shift S : f(x) f(x–1) on
while
is the spectral radius of the backward shift S–1 : f(x) (P+f)(x+1) on
Moreover, there exists a constant C, depending on , such that
for every a I. If R– < R+, we prove that there exists a bounded holomorphic function v on
such that for
the function va is the restriction of v on the line
Received: 18 May 2004 相似文献
7.
Let
be realhomogeneous functions in
ofdegree
and let bethe Borel measure on
given by
where dx denotes theLebesgue measure on
and > 0. Let T
be the convolution operator
and let
Assume that, for x 0, the followingtwo conditions hold:
vanishes only at h = 0 and
. In this paper we show that if
then E
is the empty set and if
then E
is the closed segment withendpoints
and
. Also, we give some examples. 相似文献
8.
For a class of stable planes we define a notion of isotopy equivalence with
respect to that class and prove that any two planes of a certain class of
-planes comprising all affine
-planes are isotopy equivalent. Furthermore we obtain that all affine
-planes are isotopy equivalent in the class of affine
-planes. Finally we give an example which shows that this approach cannot be easily generalized
to 2-dimensional projective planes, and we outline a different way for a
possible generalization.Received: 27 April 2001 相似文献
9.
An orthogonal complex structure on a domain in is a complex structure which is integrable and is compatible with the Euclidean metric. This gives rise to a first order
system of partial differential equations which is conformally invariant. We prove two Liouville-type uniqueness theorems for
solutions of this system, and use these to give an alternative proof of the classification of compact locally conformally
flat Hermitian surfaces first proved by Pontecorvo. We also give a classification of non-degenerate quadrics in under the action of the conformal group SO
°(1, 5). Using this classification, we show that generic quadrics give rise to orthogonal complex structures defined on the
complement of unknotted solid tori which are smoothly embedded in .
To Nigel Hitchin on the occasion of his 60th birthday.
This work was partially supported by MIUR (Metriche Riemanniane e Varietà Differenziabili, PRIN05)
and NSF Grant DMS-0503506. 相似文献
10.
P. C. Craighero R. Gattazzo M. C. Ronconi 《Annali di Matematica Pura ed Applicata》1981,129(1):81-130
Summary In this paper we classify the algebraic cubic surfaces of the affine space
is the complex field, whose algebraic curves are set-theoretic complete intersections of ; in other words surfaces such that every prime ideal of height 1in the coordinate ring [] of is the radical of a principal ideal; if is non singular in codimension 1this means that [] is semifactorial. We give the equations of such surfaces within linear isomorphisms of
providing also methods by which one can construct the equations of the surfaces cutting on its curves as set-theoretic complete intersections. Moreover for each of these surfaces we determine the minimum positive number such that every algebraic curve of with multiplicity of intersection , is complete intersection of itself with another surface
§ 8where the results are summarized). We tackle also the problem of such a classification over algebraically closed fields k different from .
Lavoro eseguito nell'ambito del G.N.S.A.G.A. del C.N.R. 相似文献
Lavoro eseguito nell'ambito del G.N.S.A.G.A. del C.N.R. 相似文献
11.
Igor Frenkel Mikhail Khovanov Catharina Stroppel 《Selecta Mathematica, New Series》2006,12(3-4):379-431
The purpose of this paper is to study categorifications of tensor products of finite-dimensional modules for the quantum group
for
. The main categorification is obtained using certain Harish-Chandra bimodules for the complex Lie algebra
. For the special case of simple modules we naturally deduce a categorification via modules over the cohomology ring of certain
flag varieties. Further geometric categorifications and the relation to Steinberg varieties are discussed.We also give a categorical
version of the quantised Schur–Weyl duality and an interpretation of the (dual) canonical bases and the (dual) standard bases
in terms of projective, tilting, standard and simple Harish-Chandra bimodules. 相似文献
12.
T. R. Riley 《Geometriae Dedicata》2005,113(1):215-229
We give a nondeterministic algorithm that expresses elements of
, for N ≥ 3, as words in a finite set of generators, with the length of these words at most a constant times the word metric. We show that the nondeterministic time-complexity of the subtractive version of Euclid’s algorithm for finding the greatest common divisor of N ≥ 3 integers a1, ..., aN is at most a constant times
. This leads to an elementary proof that for N ≥ 3 the word metric in
is biLipschitz equivalent to the logarithm of the matrix norm – an instance of a theorem of Mozes, Lubotzky and Raghunathan. And we show constructively that there exists K>0 such that for all N ≥ 3 and primes p, the diameter of the Cayley graph of
with respect to the generating set
is at most
.Mathematics Subject Classification: 20F05 相似文献
13.
We study two questions posed by Johnson, Lindenstrauss, Preiss, and
Schechtman, concerning the structure of level sets of uniform and Lipschitz
quotient mappings from
. We show that if
, is a uniform quotient mapping then for every
has
a bounded number of components, each component of
separates
and the upper bound of the number of components depends
only on
and the moduli of co-uniform and uniform continuity of
.Next we prove that all level sets of any co-Lipschitz uniformly
continuous mapping from
to
are locally connected, and we show
that for every pair of a constant
and a function
with
, there exists a natural number
, so that
for every co-Lipschitz uniformly continuous map
with a
co-Lipschitz constant
and a modulus of uniform continuity
, there
exists a natural number
and a finite set
with
card
so that for all
has exactly
components,
has exactly
components and
each component of
is homeomorphic with the real line and
separates the plane into exactly 2 components. The number and form
of components of
for
are also described - they have a
finite tree structure. 相似文献
14.
J. E. Marcos 《Czechoslovak Mathematical Journal》2003,53(3):689-706
We define various ring sequential convergences on
and
. We describe their properties and properties of their convergence completions. In particular, we define a convergence
on
by means of a nonprincipal ultrafilter on the positive prime numbers such that the underlying set of the completion is the ultraproduct of the prime finite fields
Further, we show that
is sequentially precompact but fails to be strongly sequentially precompact; this solves a problem posed by D. Dikranjan. 相似文献
15.
Nicola Visciglia 《Calculus of Variations and Partial Differential Equations》2005,24(2):167-184
We present a generalized version of the Hardy-Sobolev inequality, in which the homogeneous potential
is replaced by any potential V belonging to the Lorentz space
. We show that the best constant in these inequalities is achieved provided that
where
. We also analyze the limit case
. Finally an application to a non-linear eigenvalues problem with rough potentials is presented.Received: 19 September 2004, Accepted: 15 November 2004, Published online: 22 December 2004 相似文献
16.
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
17.
We present a (320, 88, 24)-difference set in
, the existence of which was previously open. This new difference set improves a theorem of Davis-Jedwab with the removal of the exceptional case. It also enables us to state a theorem of Schmidt on Davis-Jedwab difference sets more neatly. 相似文献
19.
Mark Pankov 《Journal of Geometry》2004,79(1-2):169-176
Let
be a finite-dimensional projective space
and
be the Grassmannian consisting of
all k-dimensional subspaces of
. In the paper we show that
transformations of
sending base subsets
to base subsets are induced by collineations of
to itself or to the dual projective space
.
This statement generalizes the main result of the authors paper [19]. 相似文献
20.
George M. Bergman 《Algebra Universalis》2005,53(2-3):357-395
Properties of several sorts of lattices of convex subsets of
are examined. The lattice of convex sets containing the origin turns out, for n > 1, to satisfy a set of identities strictly between those of the lattice of all convex subsets of
and the lattice of all convex subsets of
The lattices of arbitrary, of open bounded, and of compact convex sets in
all satisfy the same identities, but the last of these is join-semidistributive, while for n > 1 the first two are not. The lattice of relatively convex subsets of a fixed set
satisfies some, but in general not all of the identities of the lattice of “genuine” convex subsets of
To the memory of Ivan RivalReceived April 22, 2003; accepted in final form February 16, 2005.This revised version was published online in August 2005 with a corrected cover date. 相似文献