共查询到20条相似文献,搜索用时 31 毫秒
1.
M. A. Beltagy 《Rendiconti del Circolo Matematico di Palermo》1985,34(2):219-225
Local convexity and convexity of submanifolds in a general Riemannian manifold have been defined. The propblem of isometric immersion of a submanifold into a unit sphere as a locally convex submanifold has been considered. The result we have arrived at is also true for the case of convex immersion. 相似文献
2.
Bang-Yen Chen 《Geometriae Dedicata》2001,85(1-3):253-271
An isometric immersion of a Riemannian manifold into a Kählerian manifold is called slant if it has a constant Wirtinger angle. A slant submanifold is called Kählerian slant if its canonical structure is parallel. In this article, we prove a general inequality relating the mean and scalar curvatures of Kählerian slant submanifolds in a complex space form. We also classify Kählerian slant submanifolds which satisfy the equality case of the inequality. Several related results on slant submanifolds are also proved. 相似文献
3.
An isometric deformation of an Euclidean submanifold is called genuine if the submanifold cannot be included into a submanifold of larger dimension in such a way that the deformation of the former is given by an isometric deformation of the latter. The submanifold is said to be genuinely rigid if it has no genuine deformations. In this paper we study the deformation problem in codimension two for the classes of elliptic and parabolic submanifolds. In spite of having a second fundamental form as degenerate as possible without being flat, i.e., the Gauss map has rank two everywhere, our main result says that generically these submanifolds are genuinely rigid. An additional unexpected deformation phenomenon for elliptic submanifolds carrying a Kaehler structure is described. 相似文献
4.
Li Haizhong Ma Hui Van der Veken Joeri Vrancken Luc Wang Xianfeng 《中国科学 数学(英文版)》2020,63(8):1441-1462
We introduce a structural approach to study Lagrangian submanifolds of the complex hyperquadric in arbitrary dimension by using its family of non-integrable almost product structures.In particular,we define local angle functions encoding the geometry of the Lagrangian submanifold at hand.We prove that these functions are constant in the special case that the Lagrangian immersion is the Gauss map of an isoparametric hypersurface of a sphere and give the relation with the constant principal curvatures of the hypersurface.We also use our techniques to classify all minimal Lagrangian submanifolds of the complex hyperquadric which have constant sectional curvatures and all minimal Lagrangian submanifolds for which all local angle functions,respectively all but one,coincide. 相似文献
5.
Every affine map between two affinely connected manifolds is the composition of an affine submersion and an affine immersion; and the inverse image of an autoparallel submanifold by such maps is the union of autoparallel submanifolds. Furthermore, the Lie group of all affine transformations of an affinely connected manifold carries the compact-open topology. 相似文献
6.
Roughly speaking, an ideal immersion of a Riemannian manifold into a space form is an isometric immersion which produces the least possible amount of tension from the ambient space at each point of the submanifold. Recently, B.-Y. Chen classified Lagrangian immersions in complex space forms, which are ideal. In the present paper, we investigate ideal C-totally real submanifolds in a Sasakian space form. Mathematics Subject Classification (2000) 53C40, 53C25 相似文献
7.
SkewCRSubmanifoldsofaSasakianManifoldLiuXimin(刘西民)(DepartmentofMathematics,NankaiUniversity,Tianjin,300071)LiangXiquan(梁希泉)(I... 相似文献
8.
Alfonso Carriazo Luis M. Ferná ndez 《Proceedings of the American Mathematical Society》2004,132(11):3327-3336
In this paper we present an interesting relationship between graph theory and differential geometry by defining submanifolds of almost Hermitian manifolds associated with certain kinds of graphs. We show some results about the possibility of a graph being associated with a submanifold and we use them to characterize CR-submanifolds by means of trees. Finally, we characterize submanifolds associated with graphs in a four-dimensional almost Hermitian manifold.
9.
Bang-yen Chen 《Monatshefte für Mathematik》1981,91(4):257-274
LetN be a real submanifold in a complex manifoldM. If the maximal complex subspaces of the tangent spaces ofM contained in the tangent spaces ofN are of constant dimension and they define a differentiable distribution, thenN is called a generic submanifold. The class of generic submanifold includes all real hypersurfaces, complex submanifolds, totally real submanifolds andCR-submanifolds. In this paper we initiate a study of generic submanifolds in a Kähler manifold from differential geometric point of view. Some fundamental results in this respect will be obtained. 相似文献
10.
Fereshteh Malek Mohammad Bagher Kazemi Balgeshir 《Mediterranean Journal of Mathematics》2013,10(2):1023-1033
In this paper we introduce the notion of slant submanifold of an almost contact metric 3-structure manifold. We give some examples and characterize these submanifolds. Moreover, Sasakian slant submanifolds of an almost contact 3-structure manifold are defined and studied. We also establish a sharp inequality including the squared mean curvature and Ricci curvature of a Sasakian slant submanifold. 相似文献
11.
聂昌雄 《数学年刊A辑(中文版)》2015,36(1):59-68
[Nie C X,Wu C X,Regular submanifolds in the conformal space Q_p~n,ChinAnn Math,2012,33B(5):695-714]中研究了共形空间Q_s~n中的正则子流形,并引入了共形空间Q_s~n中的子流形理论.本文作者将分类共形空间Q_s~n中的Blaschke拟全脐子流形,证明伪Riemann空间形式中具有常数量曲率和平行的平均曲率向量场的正则子流形是共形空间中的Blaschke拟全脐子流形;反之,共形空间中的Blaschke拟全脐子流形共形等价于伪Riemann空间形式中具有常数量曲率和平行的平均曲率向量场的正则子流形.这一结论可看作是共形空间Q_s~n中共形迷向子流形分类定理的推广. 相似文献
12.
Heiko Ewert 《Proceedings of the American Mathematical Society》1998,126(8):2443-2452
A submanifold in a symmetric space is called equifocal if it has a globally flat abelian normal bundle and its focal data is invariant under normal parallel transportation. This is a generalization of the notion of isoparametric submanifolds in Euclidean spaces. To each equifocal submanifold, we can associate a Coxeter group, which is determined by the focal data at one point. In this paper we prove that an equifocal submanifold in a simply connected compact symmetric space is a non-trivial product of two such submanifolds if and only if its associated Coxeter group is decomposable. As a consequence, we get a similar splitting result for hyperpolar group actions on compact symmetric spaces. These results are an application of a splitting theorem for isoparametric submanifolds in Hilbert spaces by Heintze and Liu.
13.
D. Kleinbock 《Geometric And Functional Analysis》2003,13(2):437-466
It was proved in the paper [KM1] that the properties of almost all
points of being not very well (multiplicatively) approximable are
inherited by nondegenerate in (read: not contained in a proper
affine subspace) smooth submanifolds. In this paper we consider submanifolds
which are contained in proper a.ne subspaces, and prove
that the aforementioned Diophantine properties pass from a subspace
to its nondegenerate submanifold. The proofs are based on a correspondence
between multidimensional Diophantine approximation and
dynamics of lattices in Euclidean spaces.
Submitted: March 2002; Revision: August 2002 相似文献
14.
Jiří Lebl 《Journal of Geometric Analysis》2007,17(2):321-341
A local uniqueness property of holomorphic functions on real-analytic nowhere minimal CR submanifolds of higher codimension
is investigated. A sufficient condition called almost minimality is given and studied. A weaker necessary condition, being
contained a possibly singular real-analytic Levi-flat hypersurface is studied and characterized. This question is completely
resolved for algebraic submanifolds of codimension 2 and a sufficient condition for noncontainment is given for non algebraic
submanifolds. As a consequence, an example of a submanifold of codimension 2, not biholomorphically equivalent to an algebraic
one, is given. We also investigate the structure of singularities of Levi-flat hypersurfaces. 相似文献
15.
A sphere of dimension 4n+3 admits three Sasakian structures and it is natural to ask if a submanifold can be an integral submanifold for more than one of the contact structures. In the 7-sphere it is possible to have curves which are Legendre curves for all three contact structures and there are 2 and 3-dimensional submanifolds which are integral submanifolds of two of the contact structures. One of the results here is that if a 3-dimensional submanifold is an integral submanifold of one of the Sasakian structures and invariant with respect to another, it is an integral submanifold of the remaining structure and is a principal circle bundle over a holmophic Legendre curve in complex projective 3-space. 相似文献
16.
L. Verhóczki 《Periodica Mathematica Hungarica》1995,31(1):71-83
In the present paper parallel submanifolds and focal points of a given submanifold with flat normal bundle are discussed provided that the ambient space has constant sectional curvature. We present shape operators of parallel submanifolds with respect to arbitrary normal vectors. Furthermore, we prove that the focal points of a submanifold with flat normal bundle form totally geodesic hypersurfaces in the normal submanifolds.Supported by Hungarian Nat. Found. for Sci. Research Grant No. 1615 (1991).Dedicated to Professor J. Strommer on the occasion of his 75th birthday 相似文献
17.
Claudio Gorodski 《Proceedings of the American Mathematical Society》2004,132(8):2441-2447
We show that a totally geodesic submanifold of a symmetric space satisfying certain conditions admits an extension to a minimal submanifold of dimension one higher, and we apply this result to construct new examples of complete embedded minimal submanifolds in simply connected noncompact globally symmetric spaces.
18.
Miroslava ANTIC Mirjana DJORIC Luc VRANCKEN 《数学学报(英文版)》2006,22(5):1557-1564
In this paper, we study Lagrangian submanifolds of the nearly Kaehler 6-sphere. We derive a pinching result for the Ricci curvature of such submanifolds thus providing a characterisation of the totally geodesic submanifold. Our pinching result improves a previous result obtained by H. Li. 相似文献
19.
本文研究球空间中子流形的共形高斯映射,用Moebius不变量刻划了该映射 为调和映射的条件.作为特例,指出球空间的2维子流形的共形高斯映射是调和映射 当且仅当该子流形是Willmore子流形. 相似文献
20.
Generic Submanifolds 总被引:2,自引:0,他引:2
Summary In this paper we give some examples of generic submanifolds of complex space forms and prove some theorems which give the characterizations of these examples. For this purpose we study the relations between a submanifold of a Kählerian manifold and a submanifold of a Sasakian manifold by using the method of Riemannian fibre bundles. 相似文献