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1.
A submanifold M
n
r
of Minkowski space
is said to be of restricted type if its shape operator with respect to the mean curvature vector is the restriction of a fixed linear transformation of
to the tangent space of M
n
r
at every point of M
n
r
. In this paper we completely classify hypersurfaces of restricted type in
. More precisely, we prove that a hypersurface of
is of restricted type if and only if it is either a minimal hypersurface, or an open part of one of the following hypersurfaces: S
k
×
, S
k
1
×
, H
k
×
, S
n
1
, H
n
, with 1kn–1, or an open part of a cylinder on a plane curve of restricted type.This work was done when the first and fourth authors were visiting Michigan State University.Aangesteld Navorser N.F.W.O., Belgium. 相似文献
2.
A Sasakian structure
=(\xi,\eta,\Phi,g) on a manifold Mis called positiveif its basic first Chern class c1(
) can be represented by a positive (1,1)-form with respect to its transverse holomorphic CR-structure. We prove a theorem that says that every positive Sasakian structure can be deformed to a Sasakian structure whose metric has positive Ricci curvature. This provides us with a new technique for proving the existence of positive Ricci curvature metrics on certain odd dimensional manifolds. As an example we give a completely independent proof of a result of Sha and Yang that for every nonnegative integer kthe 5-manifolds k#(S
2×S
3) admits metrics of positive Ricci curvature. 相似文献
3.
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
4.
Natalie M. Priebe 《Geometriae Dedicata》2000,79(3):239-265
In this paper, a technique for analyzing levels of hierarchy in a tiling
of Euclidean space is presented. Fixing a central configuration P of tiles in
, a `derived Voronoï' tessellation
P is constructed based on the locations of copies of P in
. A family of derived Voronoï tilings
is formed by allowing the central configurations to vary through an infinite number of possibilities. The family
will normally be an infinite one, but we show that for a self-similar tiling
it is finite up to similarity. In addition, we show that if the family
is finite up to similarity, then
is pseudo-self-similar. The relationship between self-similarity and pseudo-self-similarity is not well understood, and this is the obstruction to a complete characterization of self-similarity via our method. A discussion and conjecture on the connection between the two forms of hierarchy for tilings is provided. 相似文献
5.
Orazio Puglisi 《Geometriae Dedicata》1996,63(1):95-112
In this paper we describe the structure and the conjugacy classes of Sylow p-subgroups of FGL(V,
), the group of finitary
-automorphisms of the
-vector space V.The Author is member of the GNSAGA. 相似文献
6.
Daniel T. Wise 《Geometriae Dedicata》2002,92(1):59-62
This note describes an example of a compact aspherical 2-complex X with a covering space
, such that
is finitely presented but
has no compact core.I thank John Stallings for being my 'Senior Scientist' in 1996–1997, and for many superimaginative e-mails that led to this relationship. 相似文献
7.
We study the filling length function for a finite presentation of a group , and interpret this function as an optimal bound on the length of the boundary loop as a van Kampen diagram is collapsed to the basepoint using a combinatorial notion of a null-homotopy. We prove that filling length is well behaved under change of presentation of . We look at 'AD-pairs' (f,g) for a finite presentation
: that is, an isoperimetric function f and an isodiametric function g that can be realised simultaneously. We prove that the filling length admits a bound of the form [g+1][log (f+1)+1] whenever (f,g) is an AD-pair for
. Further we show that (up to multiplicative constants) if
is an isoperimetric function (
) for a finite presentation then (
) is an AD-pair. Also we prove that for all finite presentations filling length is bounded by an exponential of an isodiametric function.Partially supported by NSF grant DMS-9800158Supported by EPSRC Award No. 98001683 and Corpus Christi College, Oxford. 相似文献
8.
Vladimir Rovenski 《Geometriae Dedicata》2006,121(1):187-203
The paper continues our (in collaboration with A. Borisenko [J. Differential Geom. Appl. 20 p., to appear]) discovery of the new classes of $(k,\varepsilon)The paper continues our (in collaboration with A. Borisenko [J. Differential Geom. Appl. 20 p., to appear]) discovery of the
new classes of
-saddle,
-parabolic, and
-convex submanifolds (
). These are defined in terms of the eigenvalues of the 2nd fundamental forms of each unit normal of the submanifold, extending
the notion of k-saddle, k-parabolic, k-convex submanifolds (
). It follows that the definition of
-saddle submanifolds is equivalent to the existence of
-asymptotic subspaces in the tangent space. We prove non-embedding theorems of
-saddle submanifolds, theorems about 1-connectedness and homology groups of these submanifolds in Riemannian spaces of positive
(sectional or qth Ricci) curvature, in particular, spherical and projective spaces. We apply these results to submanifolds with ‘small’ normal
curvature,
, and for submanifolds with extrinsic curvature
(resp., non-positive) and small codimension, and include some illustrative examples. The results of the paper generalize
theorems about totally geodesic, minimal and k-saddle submanifolds by Frankel; Borisenko, Rabelo and Tenenblat; Kenmotsu and Xia; Mendon?a and Zhou.
相似文献
9.
ALAIN HÉNAUT 《Geometriae Dedicata》1997,65(1):89-101
A d-web in (
,0) is given by d complex analytic foliations of codimension one in (
,0) which are in general position. A d-web
in (
,0) is linear if all the leaves are (pieces of) hyperplanes in
and
is algebraic if it is associated, by duality, to a nondegenerate algebraic curve in
of degree d. We characterize linear webs in (
,0). We give explicit conditions under which a linear d-web in (
,0) is algebraic and we obtain equations for
in this case. Some related problems are discussed and some questions are posed. 相似文献
10.
Let (M,F) and (M,F) be two (compact or not) foliated manifolds, C
F
(M, M) the space of smooth maps which send leaves into leaves. In this paper we prove that C
F
(M, M) admits a structure of an infinite-dimensional manifold modeled on LF-spaces, provided that F is a Riemannian foliation or, more generally, when it admits an adapted local addition. 相似文献
11.
Let (M,
, g) be a sub-Riemannian manifold (i.e. M is a smooth manifold,
is a smooth distribution on M and g is a smooth metric defined on
) such that the dimension of M is either 3 or 4 and
is a contact or odd-contact distribution, respectively. We construct an adapted connection on M and use it to study the equivalence problem. Furthermore, we classify the 3-dimensional sub-Riemannian manifolds which are sub-homogeneous and show the relation to Cartan's list of homogeneous CR manifolds. Finally, we classify the 4-dimensional sub-Riemannian manifolds which are sub-symmetric. 相似文献
12.
We show that every sub-weak embedding of any singular (degenerate or not) orthogonal or unitary polar space of non-singular rank at least 3 in a projective space PG
,
a commutative field, is the projection of a full embedding in some subspace PG
of PG
, where PG
contains PG
and
is a subfield of
. The same result is proved in the symplectic case under the assumption that the field over which the polarity is defined is perfect if the characteristic is 2 and if each secant line of the embedded polar space contains exactly two points of . This completes the classification of all sub-weak embeddings of orthogonal, symplectic and unitary polar spaces (singular or not; degenerate or not) of non-singular rank at least 3 and defined over a commutative field
, where in the characteristic 2 case
is perfect if the polar space is symplectic and the degree of the embedding is 2. 相似文献
13.
Alain Rivière 《Geometriae Dedicata》2001,85(1-3):217-235
For a separable Hilbert space E whose dimension is 2 and for an open subset of E, not empty and different from E, let
be the set of all points of which have at least two projections on the close set E\, and let
be the set of all the centres of the open balls contained in and which are maximal for inclusion. We show that the Hausdorff dimension dimH(
) of
may be any real value s such that 0sdim E; we also show that can be chosen so that
is everywhere dense in and so that we have dimH(
)=1.Associons à un ouvert d'un espace de Hilbert séparable E de dimension 2, non vide et distinct de E, l'ensemble
des points de admettant plusieurs projections sur le fermé E\, et l'ensemble
des centres des boules ouvertes inclues dans et maximales pour l'inclusion. Nous montrons d'une part que la dimension de Hausdorff dimH(
) de
peut prendre toute valeur réelle s telle que 0sdim E, et d'autre part qu'on peut choisir de sorte que
soit dense dans et qu'on ait dimH(
)=1. 相似文献
14.
Necdet Güner 《Geometriae Dedicata》1996,63(1):17-23
Let N=G/ be a compact nilmanifold, G a connected, simply connected, nilpotent Lie group with its discrete subgroup and Lie algebra
. Let I* (
) denote the invariant differential forms on
.If I* (
) H* (
) is an injective map, then G is abelian and N is a torus. Furthermore, N has a formal minimal model. If N is an even-dimensional compact nilmanifold, it has a Kähler structure and invariant symplectic structure if and only if I* (
) H* (
) is injective. 相似文献
15.
Rudolf Scharlau 《Geometriae Dedicata》1987,24(1):77-84
Following earlier work of Tits [8], this paper deals with the structure of buildings which are not necessarily thick; that is, possessing panels (faces of codimension 1) which are contained in two chambers, only. To every building , there is canonically associated a thick building
whose Weyl group W(
) can be considered as a reflection subgroup of the Weyl group W() of . One can reconstruct from
together with the embedding W(
) W(). Conversely, if
is any thick building and W any reflection group containing W(
) as a reflection subgroup, there exists a weak building with Weyl group W and associated thick building
. 相似文献
16.
We study level surfaces of non-degenerate functions inR
n+1. Such level surfaces are non-degenerate in the sense of affine differential geometry. In affine differential geometry, the affine normal plays an important role for the study of a non-degenerate hypersurface. In this note, being motivated by Koszul's work we take a canonical vector field
for level surfaces of a non-degenerate function and give certain characterizations of when
is transversal, by the shape operatorS, the transversal connection , and consider the difference between
and the affine normal. 相似文献
17.
TATSUYA MARUTA 《Geometriae Dedicata》1997,65(3):299-304
Let
be the smallest integer n for which there exists a linear code of length n, dimension k and minimum Hamming distance d over the Galois field GF(q). In this paper we determine
for
for all q, using a geometric method. 相似文献
18.
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
19.
Yutaka Hiramine 《Geometriae Dedicata》1993,48(2):139-189
In this paper we consider finite nets of orderq
2 and degreeq + 1 which admit GL(2,q). Our main result says that if a net
of orderq
2 and degreeq + 1 admits a collineation group with a point-regular normal subgroupT such that /T GL(2,q), then
is isomorphic to a regulus net, a twisted regulus net, a Hering net, or
. Except in the last one, each of them corresponds to a surface in PG(3,q) obtained from a homogeneous polynomial in two variables. 相似文献
20.
Suppose G is a connected, simple, real Lie group with
-rank(G) 2, M is an ergodic G-space with invariant probability measure , and : G × M Homeo(
) is a Borel cocycle. We use an argument of É. Ghys to show that there is a G-invariant probability measure on the skew product M ×
, such that the projection of to M is . Furthermore, if (G × M) Diff1(
), then can be taken to be equivalent to × , where is Lebesgue measure on
; therefore, is cohomologous to a cocycle with values in the isometry group of
. 相似文献