共查询到20条相似文献,搜索用时 15 毫秒
1.
Antonio J. Di Scala 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2009,79(1):37-46
Let M⊂ℝ
n
be a submanifold of a euclidean space. A vector d∈ℝ
n
is called a helix direction of M if the angle between d and any tangent space T
p
M is constant. Let ℋ(M) be the set of helix directions of M. If the set ℋ(M) contains r linearly independent vectors we say that M is a weak r-helix. We say that M is a strong r-helix if ℋ(M) is a r-dimensional linear subspace of ℝ
n
. For curves and hypersurfaces both definitions agree. The object of this article is to show that these definitions are not
equivalent. Namely, we construct (non strong) weak 2-helix surfaces of ℝ4.
The author is supported by the Project M.I.U.R. “Riemann Metrics and Differentiable Manifolds” and by G.N.S.A.G.A. of I.N.d.A.M.,
Italy. 相似文献
2.
3.
Sergio Console 《Annals of Global Analysis and Geometry》1994,12(1):313-334
For a class of submanifolds of N, the infinitesimally homogeneous ones, the second fundamental form and itss-times iterated derivativessk+1 at any fixed point determine the immersion uniquely. The integerk>0 will be called the extrinsic Singer invariant. Any infinitesimally homogeneous submanifoldM (which is not necessarily complete) is an open part of a globally homogeneous (complete) submanifold. Indeed, the infinitesimal data at any pointp, determine, canonically, a Lie subgroupG of the isometry group of
N
, whose orbit atp is a complete submanifold that extendsM.
Work partially supported by the GNSAGA of CNR and by the MURST of Italy 相似文献
4.
Austere submanifolds and arid submanifolds constitute respectively two different classes of minimal submanifolds in finite dimensional Riemannian manifolds. In this paper we introduce the concepts of these submanifolds into a class of proper Fredholm (PF) submanifolds in Hilbert spaces, discuss their relation and show examples of infinite dimensional austere PF submanifolds and arid PF submanifolds in Hilbert spaces. We also mention a classification problem of minimal orbits in hyperpolar PF actions on Hilbert spaces. 相似文献
5.
Valentin Burcea 《数学学报(英文版)》2017,33(1):1-20
Let(z_(11),..., z_(1N),..., z_(m1),..., z_(mN), w_(11),..., w_(mm)) be the coordinates in C~(mN) +m~2. In this note we prove the analogue of the Theorem of Moser in the case of the real-analytic submanifold M defined as follows W = ZZ~t+ O(3),where W = {w_(ij)}_(1≤i,j≤m)and Z = {z_(ij) }_(1≤i≤m, 1≤j≤N). We prove that M is biholomorphically equivalent to the model W = ZZ~t if and only if is formally equivalent to it. 相似文献
6.
Rong-mei CAO~ 《中国科学A辑(英文版)》2007,50(9):1334-1338
Let M be an m-dimensional analytic manifold in R~n.In this paper,we prove that almost all vectors in M (in the sense of Lebesgue measure) are Diophantine if there exists one Diophantine vector in M. 相似文献
7.
In this paper, we investigate complete curvature-adapted submanifolds with maximal flat section and trivial normal holonomy group in symmetric spaces of compact type or non-compact type under a certain condition, and derive the constancy of the principal curvatures of such submanifolds. As a result, we derive that such submanifolds are isoparametric. 相似文献
8.
ZHU Fuhai & LIANG KeSchool of Mathematical Sciences LMAM Peking University Beijing China College of Mathematical Sciences LPMC Nankai University Tianjin China 《中国科学A辑(英文版)》2004,47(2):264-271
We gave a complete list of totally geodesic submanifolds of maximal rank in symmetric spaces of noncompact type. The compact cases can be obtained by the duality. 相似文献
9.
关于de Sitter空间中类空子流形的一些刚性定理 总被引:1,自引:0,他引:1
研究了deSitter空间中具有常数量曲率的类空子流形,利用活动标架的方法,证明了这类子流形的某些刚性定理,推广了已有的一些结果. 相似文献
10.
11.
A. A. Borisenko 《Mathematical Notes》1996,60(1):3-7
In this paper we consider compact multidimensional surfaces of nonpositive external curvature in a Riemannian space. If the
curvature of the underlying space is ≥ 1 and the curvature of the surface is ≤ 1, then in small codimension the surface is
a totally geodesic submanifold that is locally isometric to the sphere. Under stricter restrictions on the curvature of the
underlying space, the submanifold is globally isometric to the unit sphere.
Translated fromMatematicheskie Zametki, Vol. 60, No. 1, pp. 3–10, July, 1996. 相似文献
12.
Summary Let <InlineEquation ID=IE"4"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"5"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"6"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"7"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"8"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"9"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"10"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"11"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"12"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"13"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"14"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"15"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"16"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"17"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"18"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"19"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"20"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"21"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>M^n$
be a Riemannian $n$-manifold with $n\ge 4$. Consider the Riemannian invariant $\sigma(2)$ defined by <InlineEquation ID=IE"1"><EquationSource
Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"3"><EquationSource
Format="TEX"><![CDATA[$$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>
\sigma(2)=\tau-\frac{(n-1)\min \Ric}{n^2-3n+4}, $$ where $\tau$ is the scalar curvature of $M^n$ and $(\min \Ric)(p)$ is the
minimum of the Ricci curvature of $M^n$ at $p$. In an earlier article, B. Y. Chen established the following sharp general
inequality: $$ \sigma(2)\le \frac{n^2{(n-2)}^2}{2(n^2-3n+4)}H^2 $$ for arbitrary $n$-dimensional conformally flat submanifolds
in a Euclidean space, where $H^2$ denotes the squared mean curvature. The main purpose of this paper is to completely classify
the extremal class of conformally flat submanifolds which satisfy the equality case of the above inequality. Our main result
states that except open portions of totally geodesic $n$-planes, open portions of spherical hypercylinders and open portion
of round hypercones, conformally flat submanifolds satifying the equality case of the inequality are obtained from some loci
of $(n-2)$-spheres around some special coordinate-minimal surfaces. 相似文献
13.
V. A. Gor'kavyi 《Mathematical Notes》1997,62(5):581-585
We present necessary and sufficient conditions for a regular three-dimensional manifold in the Grassmannian manifoldG(m, m+3) to be the Gauss image of a regular 3-submanifold in (m+3)-dimensional Euclidean space form>4.
Translated fromMatemalicheskie Zametki, Vol. 62, No. 5, pp. 694–699, November, 1997.
Translated by S. K. Lando 相似文献
14.
In this note we provide a direct proof of the complete classification of conformally flat isoparametric submanifolds of Euclidean space. 相似文献
15.
In this paper, using ideas of Simons, Ros, and Savo, we prove a comparison between the spectrums of the stability operator and the Hodge–Laplacian acting on differential 1-forms on a compact minimal submanifold immersed into a Euclidean domain. 相似文献
16.
Given a closed connected manifold smoothly immersed in a complete noncompact Riemannian manifold with nonnegative sectional curvature, we estimate the intrinsic diameter of the submanifold in terms of its mean curvature field integral. On the other hand, for a compact convex surface with boundary smoothly immersed in a complete noncompact Riemannian manifold with nonnegative sectional curvature, we can estimate its intrinsic diameter in terms of its mean curvature field integral and the length of its boundary. These results are supplements of previous work of Topping, Wu-Zheng and Paeng. 相似文献
17.
Al Boggess 《Proceedings of the American Mathematical Society》1999,127(5):1427-1435
We consider the set of CR functions on a connected tube submanifold of satisfying a uniform bound on the -norm in the tube direction. We show that all such CR functions holomorphically extend to functions on the convex hull of the tube (). The -norm of the extension is shown to be the same as the uniform -norm in the tube direction of the CR function.
18.
We study the geometry of homogeneous hypersurfaces and their focal sets in complex hyperbolic spaces. In particular, we provide
a characterization of the focal set in terms of its second fundamental form and determine the principal curvatures of the
homogeneous hypersurfaces together with their multiplicities.
相似文献
19.
Zhangjie Liu 《Frontiers of Mathematics in China》2007,2(3):417-438
In this paper, we give some rigidity theorems which concern with compact minimal coisotropic submanifolds in ℂPn, compact minimal quaternionic coisotropic submanifolds in ℚPn and compact minimal hypersurfaces in P2 (Cay).
相似文献
20.
XuSenlin ChenDongmei 《分析论及其应用》2004,20(4):383-390
The purpose of this paper is to study complete space-like submanifolds with parallel mean curvature vector and flat normal bundle in a locally symmetric semi-defnite space satisfying some curvature conditions. We first give an optimal estimate of the Laplacian of the squared norm of the second fundamental form for such submanifold. Furthermore, the totally umbilical submanifolds are characterized 相似文献