共查询到20条相似文献,搜索用时 15 毫秒
1.
John R. Faulkner 《Geometriae Dedicata》1996,60(3):237-275
A new axiomatization involving incidence and remoteness of planes with nondivision coordinate rings is introduced and a coordinatization theorem is obtained. A geometric process of splitting points and lines to obtain another plane with the same coordinates is described. It is also shown that a group of Steinberg type is parametrized by a nonassociative ring. The notion of elementary basis sets for an associative ring is introduced and constructions of projective and affine planes are given. A plane with reflections determining a system of rotations is shown to have commutative, associative coordinates. 相似文献
2.
Stefan Immervoll 《Archiv der Mathematik》2006,87(5):478-480
We generalize a result of Kramer, see [7, 10.7 and 10.10], on generalized quadrangles associated with isoparametric hypersurfaces
of Clifford type to Tits buildings of type C2 derived from arbitrary isoparametric hypersurfaces with four distinct principal curvatures in spheres: two distinct points
p and q of a generalized quadrangle associated with an isoparametric hypersurface in the unit sphere of a Euclidean vector space
can be joined by a line K if and only if (p − q)/||p − q|| is a line. This line is orthogonal to K. Dually, two distinct lines L and K intersect if and only if (L − K)/||L − K|| is point.
Received: 14 October 2005 相似文献
3.
We construct new examples of embedded, complete, minimal hypersurfaces in complex hyperbolic space, including deformations of bisectors and some minimal foliations. Received: 20 March 2000 / Revised version: 21 July 2000 相似文献
4.
For hypersurfaces with regular Weingarten operator in nonflat space forms we study the relations between the intrinsic geometry of the third fundamental form metric and the extrinsic geometry of the hypersurface. We prove a theorema-egregium-type result for this metric and, in particular, give a local classification of hypersurfaces in case of an Einstein structure of this metric.Partially supported by the project 19701003 of NSFC.The geometry groops at TU Berlin and KU Leuven cooperate within the GA DGET program. 相似文献
5.
Harald Löwe 《Geometriae Dedicata》1995,58(1):45-51
We construct symmetric planes associated with an arbitrary locally compact connected nearfield
. If
is a proper nearfield, i.e.
{;;}, then the tangent translation plane of this symmetric plane is not classical. All previously known examples of symmetric planes have classical tangent translation planes.Herrn Professor Dr. H. Salzmann zum 65. Geburtstag gewidmet 相似文献
6.
Given a generalized Robertson-Walker spacetime whose warping function verifies a certain convexity condition, we classify strongly stable spacelike hypersurfaces with constant mean curvature. More precisely, we will show that given a closed, strongly stable spacelike hypersurface of with constant mean curvature H, if the warping function ? satisfying ?″?max{H?′,0} along M, then Mn is either maximal or a spacelike slice Mt0={t0}×F, for some t0∈I. 相似文献
7.
We prove that a compact, connected submanifold of the point space of a
smooth projective plane is homeomorphic to a sphere provided that
certain intersection properties with lines are satisfied. As an
application, we show that the set of absolute points of a smooth
polarity in a smooth projective plane of dimension 2l is empty or
homeomorphic to a sphere of dimension 2l - 1 or
.Received: 13 September 2002 相似文献
8.
Claudio Gorodski 《Geometriae Dedicata》1994,53(1):75-102
The purpose of this paper is to pursue to work initiated by Hsiang-Lawson and study cohomogeneity 1 minimal hypersurfaces in Euclidean spheres which are equivariant under the linear isotropy representation of a rank 3 compact symmetric space.Supported by the grant NSF DMS 90-01089 and by CNPq (Brazil) 相似文献
10.
Henrique F. de Lima Joseílson R. de Lima 《Differential Geometry and its Applications》2012,30(1):136-143
The aim of this paper is to study the uniqueness of complete hypersurfaces immersed in a semi-Riemannian warped product whose warping function has convex logarithm and such that its fiber has constant sectional curvature. By using as main analytical tool a suitable maximum principle for complete noncompact Riemannian manifolds and supposing a natural comparison inequality between the r-th mean curvatures of the hypersurface and that ones of the slices of the region where the hypersurface is contained, we are able to prove that a such hypersurface must be, in fact, a slice. 相似文献
11.
12.
Henrique F. de Lima 《Differential Geometry and its Applications》2008,26(4):445-455
In this paper we obtain a sharp height estimate concerning compact spacelike hypersurfaces Σn immersed in the (n+1)-dimensional Lorentz-Minkowski space Ln+1 with some nonzero constant r-mean curvature, and whose boundary is contained into a spacelike hyperplane of Ln+1. Furthermore, we apply our estimate to describe the nature of the end of a complete spacelike hypersurface of Ln+1. 相似文献
13.
A. Caminha 《Differential Geometry and its Applications》2006,24(6):652-659
In this paper we use the standard formula for the Laplacian of the squared norm of the second fundamental form and the asymptotic maximum principle of H. Omori and S.T. Yau to classify complete CMC spacelike hypersurfaces of a Lorentz ambient space of nonnegative constant sectional curvature, under appropriate bounds on the scalar curvature. 相似文献
14.
Bing-Le Wu 《Geometriae Dedicata》1994,50(3):247-250
In this note we prove that for eachn there are only finitely many diffeomorphism classes of compact isoparametric hypersurfaces ofS
n+1 with four distinct principal curvatures. 相似文献
15.
We characterize Hopf hypersurfaces inS
6 as open parts of geodesic hyperspheres or of tubes around almost complex curves ofS
6. 相似文献
16.
Bang-Yen Chen 《Monatshefte für Mathematik》2007,151(2):143-152
Let π : M → B be a Riemannian submersion with minimal fibers. In this article we prove the following results: (1) If M is positively curved, then the horizontal distribution of the submersion is a non-totally geodesic distribution; (2) if M is non-negatively (respectively, negatively) curved, then the fibers of the submersion have non-positive (respectively, negative)
scalar curvature; and (3) if M can be realized either as an elliptic proper centroaffine hypersphere or as an improper hypersphere in some affine space,
then the horizontal distribution is non-totally geodesic. Several applications are also presented. 相似文献
17.
The n-dimensional complex hyperquadric is a compact complex algebraic hypersurface defined by the quadratic equation in the (n+1)-dimensional complex projective space, which is isometric to the real Grassmann manifold of oriented 2-planes and is a
compact Hermitian symmetric space of rank 2. In this paper, we study geometry of compact Lagrangian submanifolds in complex
hyperquadrics from the viewpoint of the theory of isoparametric hypersurfaces in spheres. From this viewpoint we provide a
classification theorem of compact homogeneous Lagrangian submanifolds in complex hyperquadrics by using the moment map technique.
Moreover we determine the Hamiltonian stability of compact minimal Lagrangian submanifolds embedded in complex hyperquadrics
which are obtained as Gauss images of isoparametric hypersurfaces in spheres with g(= 1, 2, 3) distinct principal curvatures.
Dedicated to Professor Hajime Urakawa on his sixtieth birthday.
H. Ma was partially supported by NSFC grant No. 10501028, SRF for ROCS, SEM and NKBRPC No. 2006CB805905. Y. Ohnita was partially
supported by JSPS Grant-in-Aid for Scientific Research (A) No. 17204006. 相似文献
18.
Joachim Otte 《Geometriae Dedicata》1995,58(2):203-212
A projective plane is called smooth if both the point space and the line space are smooth manifolds such that the geometric operations are smooth. We prove that every smooth projective translation plane is isomorphic to one of the classical planes over , , or
.Dedicated to Professor Dr. H. Salzmann on the occasion of his 65th birthday 相似文献
19.
20.
Knut Smoczyk 《manuscripta mathematica》1998,95(1):225-236
Under the assumption of two a-priori bounds for the mean curvature, we are able to generalize a recent result due to Huisken
and Sinestrari [8], valid for mean convex surfaces, to a much larger class. In particular we will demonstrate that these a-priori
bounds are satisfied for a class of surfaces including meanconvex as well as starshaped surfaces and a variety of manifolds
that are close to them. This gives a classification of the possible singularities for these surfaces in the casen=2. In addition we prove that under certain initial conditions some of them become mean convex before the first singularity
occurs. 相似文献