共查询到20条相似文献,搜索用时 15 毫秒
1.
Franki Dillen 《Geometriae Dedicata》1989,32(1):81-92
In this paper we establish an affine equivalence theorem for affine submanifolds of the real affine space with arbitrary codimension. Next, this theorem is used to prove the classical congruence theorem for submanifolds of the Euclidean space, and to prove some results on affine hypersurfaces of the real affine space.Research Assistant of the National Fund for Scientific Research (Belgium). 相似文献
2.
We study the equi-centro-affine invariants of plane curves from the view point of the singularity theory of smooth functions. We define the notion of the equi-centro-affine pre-evolute and pre-curve and establish the relationship between singularities of these objects and geometric invariants of plane curves. 相似文献
3.
A.G. García M.A. Hernández-Medina G. Pérez-Villalón 《Journal of Computational and Applied Mathematics》2009
Assume that a sequence of samples of a filtered version of a function in a shift-invariant space is given. This paper deals with the existence of a sampling formula involving these samples and having reconstruction functions with compact support. This is done in the light of the generalized sampling theory by using the oversampling technique. A necessary and sufficient condition is given in terms of the Smith canonical form of a polynomial matrix. Finally, we prove that the aforesaid oversampled formulas provide nice approximation schemes with respect to the uniform norm. 相似文献
4.
Jeanne N. Clelland 《Differential Geometry and its Applications》2006,24(6):628-651
We define the notion of sub-Finsler geometry as a natural generalization of sub-Riemannian geometry with applications to optimal control theory. We compute a complete set of local invariants, geodesic equations, and the Jacobi operator for the three-dimensional case and investigate homogeneous examples. 相似文献
5.
We extend an original idea of Calabi for affine maximal surfaces and define
a sextic holomorphic differential form for affine surfaces with constant affine mean
curvature. We get some rigidity results for affine complete surfaces by using this
sextic holomorphic form.
Received: 17 May 2003 相似文献
6.
In this paper, we propose a definition of a general mixed Lp Affine surface area, ?n ≠ p ∈ ?, for multiple functions. Our definition is di?erent from and is “dual” to the one in [11] by Caglar and Ye. In particular, our definition makes it possible to establish an integral formula for the general mixed Lp Affine surface area of multiple functions (see Theorem 3.1 for more precise statements). Properties of the newly introduced functional are proved such as affine invariance, and related affine isoperimetric inequalities are proved. 相似文献
7.
V. Miquel 《Geometriae Dedicata》1984,15(3):261-267
Let D be the characteristic connection of an almost-Hermitian manifold, V
D
m
(r) the volume of a small geodesic ball for the connection D and C
C
D
1
the first non-trivial term of the Taylor expansion of V
D
m
(r). NK-manifolds are characterized in terms of C
C
D
1
and a family of Hermitian manifolds for which
M
C
C
D
1
dvol is a spectral invariant is given and one proves that C
C
D
1
and the spectrum of the complex Laplacian, together, determine the class in which a compact Hermitian manifold lines. 相似文献
8.
We call a latticeL strictly locally order-affine complete if, given a finite subsemilatticeS ofL
n, every functionf: S L which preserves congruences and order, is a polynomial function. The main results are the following: (1) all relatively complemented lattices are strictly locally order-affine complete; (2) a finite modular lattice is strictly locally order-affine complete if and only if it is relatively complemented. These results extend and generalize the earlier results of D. Dorninger [2] and R. Wille [9, 10]. 相似文献
9.
Benjamin McKay 《Differential Geometry and its Applications》2006,24(6):670-689
We uncover the lowest order differential invariants of Lagrangian submanifolds under affine symplectic maps, and find out what happens when they are constant. 相似文献
10.
Guojun Yang 《Differential Geometry and its Applications》2011,29(4):606-614
This paper studies some properties of projective changes in spray and Finsler geometry. Firstly, it obtains a comparison theorem on Ricci curvature for projectively related Finsler metrics. Secondly, it studies the properties of a class of projectively flat sprays, which particularly shows that there exist many isotropic sprays that cannot be induced by any (even singular) Finsler metrics. 相似文献
11.
12.
K. L. Duggal 《Acta Appl Math》1986,7(3):211-223
As a recent excellent example of mutual interplay between the Cauchy-Riemann structure and physical spacetime geometry, we present, in this paper, a few fresh ideas on this fruitful relationship with respect to the conformal geometry and the groups of motions of Lorentzian manifolds. 相似文献
13.
Jun Ichi Fujii 《Linear algebra and its applications》2010,432(1):318-558
Recently Hiai-Petz (2009) [10] discussed a parametrized geometry for positive definite matrices with a pull-back metric for a diffeomorphism to the Euclidean space. Though they also showed that the geodesic is a path of operator means, their interest lies mainly in metrics of the geometry. In this paper, we reconstruct their geometry without metrics and then we show their metric for each unitarily invariant norm defines a Finsler one. Also we discuss another type of geometry in Hiai and Petz (2009) [10] which is a generalization of Corach-Porta-Recht’s one [3]. 相似文献
14.
In this paper we study the regularity of closed, convex surfaces which achieve maximal affine area among all the closed, convex
surfaces enclosed in a given domain in the Euclidean 3-space. We prove the C1,α regularity for general domains and C1,1 regularity if the domain is uniformly convex.
This work is supported by the Australian Research Council. Research of Sheng was also supported by ZNSFC No. 102033.
On leave from Zhejiang University. 相似文献
15.
IfM
2 is a nondegenerate surface in a 4-dimensional Riemannian manifold
, then there is a natural affine metricg defined onM
2. It is shown that this affine metricg is conformal to the induced Riemannian metric onM
2 if and only ifM
2 is a minimal submanifold of
in the usual Riemannian sense. If the conformal factor is a constant, then the two metrics are said to be homothetic. It is shown that there does not exist a nondegenerate surface in Euclidean space 4 or hyperbolic spaceH
4 whose affine metric is homothetic to the induced Riemannian metric. Furthermore, ifM
2 is a nondegenerate surface in the standard 4-sphereS
4 whose affine metric is homothetic to the induced Riemannian metric, thenM
2 is a Veronese surface.T. Cecil was supported by NSF Grant No. DMS-9101961. 相似文献
16.
Generic singularities of envelopes of families of chords and bifurcations of affine equidistants defined by a pair of a curve and a surface in R3 are classified. The chords join pairs of points of the curve and the surface such that the tangent line to the curve is parallel to the tangent plane to the surface. The classification contains singularities of stable Lagrange and Legendre projections, boundary singularities and some less known classes appearing at the points of the surface and the curve themselves. 相似文献
17.
We discuss the Ribaucour transformation of Legendre (contact) maps in its natural context: Lie sphere geometry. We give a simple conceptual proof of Bianchi's original Permutability Theorem and its generalisation by Dajczer-Tojeiro as well as a higher dimensional version with the combinatorics of a cube. We also show how these theorems descend to the corresponding results for submanifolds in space forms. 相似文献
18.
Barbara Opozda 《Geometriae Dedicata》1995,55(2):141-163
We present a new approach — which is more general than the previous ones — to the affine differential geometry of complex hypersurfaces inC
n+1. Using this general approach we study some curvature conditions for induced connections.The research supported by Alexander von Humboldt Stiftung and KBN grant no. 2 P30103004. 相似文献
19.
Fang Jia 《Differential Geometry and its Applications》2005,22(2):199-214
Let be a locally strongly convex hypersurface, given by a strictly convex function xn+1=f(x1,…,xn) defined in a convex domain Ω⊂An. We consider the Riemannian metric G# on M, defined by . In this paper we prove that if M is a locally strongly convex surface with constant affine mean curvature and if M is complete with respect to the metric G#, then M must be an elliptic paraboloid. 相似文献
20.
Hirohiko Shima 《Geometriae Dedicata》1995,56(2):177-184
In our previous paper [4] we have investigated level surfaces of a non-degenerate function in a real affine space A
n+1 by using the gradient vector field
. We gave characterizations of by means of the shape operatorS, the transversal connection , and studied the difference between
and the affine normal. In particular we showed that a graph defined by a non-degenerate function satisfiesS=0 and =0. In this paper we consider harmonic gradient mappings of level surfaces and apply these results to a certain problem which is similar to the affine Bernstein problem conjectured by S. S. Chern [3]. 相似文献