共查询到20条相似文献,搜索用时 15 毫秒
1.
Giovanni Calvaruso Reinier Storm Joeri Van der Veken 《Mathematische Nachrichten》2020,293(9):1707-1729
We classify totally geodesic and parallel hypersurfaces of four-dimensional non-reductive homogeneous pseudo-Riemannian manifolds. 相似文献
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We bridge between submanifold geometry and curve theory. In the first half of this paper we classify real hypersurfaces in a complex projective plane and a complex hyperbolic plane all of whose integral curves γ of the characteristic vector field are totally real circles of the same curvature which is independent of the choice of γ in these planes. In the latter half, we construct real hypersurfaces which are foliated by totally real (Lagrangian) totally geodesic submanifolds in a complex hyperbolic plane, which provide one of the examples obtained in the classification. 相似文献
3.
Ara Basmajian 《Inventiones Mathematicae》1994,117(1):207-225
Summary We show that a closed embedded totally geodesic hypersurface in a hyperbolic manifold has a tubular neighborhood whose width only depends on the area of the hypersurface. Namely, we construct a tubular neighborhood function and show that an embedded closed totally geodesic hypersurface in a hyperbolic manifold has a tubular neighborhood whose width only depends on the area of the hypersurface (and hence not on the geometry of the ambient manifold). The implications of this result for volumes of hyperbolic manifolds is discussed. In particular, we show that ifM is a hyperbolic 3-manifold containingn rank two cusps andk disjoint totally geodesic embedded closed surfaces, then the volume ofM is bigger than
. We also derive a (hyperbolic) quantitative version of the Klein-Maskit combination theorem (in all dimensions) for free products of fuchsian groups. Using this last result, we construct examples to illustrate the qualitative sharpness of our tubular neighborhood function in dimension three. As an application of our results we give an eigenvalue estimate.Oblatum IX-1992 & 18-VIII-1993Research supported in part by NSF Grant DMS-9207019 相似文献
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Masahiro Ooguri 《Differential Geometry and its Applications》2007,25(1):56-77
We give a complete classification of 3-dimensional locally homogeneous Blaschke hypersurfaces whose affine shape operators are diagonalizable and have two or three distinct real eigenvalues. 相似文献
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Mohammed Guediri 《Transactions of the American Mathematical Society》2003,355(2):775-786
The main purpose of this paper is to prove that there are no closed timelike geodesics in a (compact or noncompact) flat Lorentz 2-step nilmanifold where is a simply connected 2-step nilpotent Lie group with a flat left-invariant Lorentz metric, and a discrete subgroup of acting on by left translations. For this purpose, we shall first show that if is a 2-step nilpotent Lie group endowed with a flat left-invariant Lorentz metric then the restriction of to the center of is degenerate. We shall then determine all 2-step nilpotent Lie groups that can admit a flat left-invariant Lorentz metric. We show that they are trivial central extensions of the three-dimensional Heisenberg Lie group . If is one such group, we prove that no timelike geodesic in can be translated by an element of By the way, we rediscover that the Heisenberg Lie group admits a flat left-invariant Lorentz metric if and only if
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In this paper we determine the structure of an embedded totally geodesic hypersurfaceF or, more generally, of a totally geodesic hypersurfaceF without selfintersections under arbitrarily small angles in a compact manifoldM of nonpositive sectional curvature. Roughly speaking, in the case of locally irreducibleM the result says thatF has only finitely many ends, and each end splits isometrically asK×(0, ∞), whereK is compact.
This article was processed by the author using the Springer-Verlag TEX PJour1g macro package 1991. 相似文献
11.
We prove that a four-dimensional generalized symmetric space does not admit any non-degenerate hypersurfaces with parallel second fundamental form, in particular non-degenerate totally geodesic hypersurfaces, unless it is locally symmetric. However, spaces which are known as generalized symmetric spaces of type C do admit non-degenerate parallel hypersurfaces and we verify that they are indeed symmetric. We also give a complete and explicit classification of all non-degenerate totally geodesic hypersurfaces of spaces of this type. 相似文献
12.
Gautier Berck 《Mathematische Annalen》2009,343(4):955-973
Using the symplectic definition of the Holmes-Thompson volume we prove that totally geodesic submanifolds of a Finsler manifold
are minimal for this volume. Thanks to well suited technics the minimality of totally geodesic hypersurfaces (see álvarez
Paiva and Berck in Adv Math 204(2):647–663, 2006) and 2-dimensional totally geodesic surfaces (see álvarez Paiva and Berck
in Adv Math 204(2):647–663, 2006, Ivanov in Algebra i Analiz 13(1)26–38, 2001) had already been proved. However the corresponding
statement for the Hausdorff measure is known to be wrong even in the simplest case of totally geodesic 2-dimensional surfaces
in a 3-dimensional Finsler manifold (see álvarez Paiva and Berck in Adv Math 204(2):647–663, 2006). 相似文献
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Partially supported by an NSF grant. 相似文献
14.
A. Yampolsky 《Acta Mathematica Hungarica》2003,101(1-2):93-112
We prove that the Hopf vector field is unique among geodesic unit vector fields on spheres such that the submanifold generated by the field is totally geodesic in the unit tangent bundle with Sasaki metric. As an application, we give a new proof of stability (instability) of the Hopf vector field with respect to volume variation using standard approach from the theory of submanifolds and find exact boundaries for the sectional curvature of the Hopf vector field. 相似文献
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A Lie algebra L is called 2-step nilpotent if L is not abelian and [L,L] lies in the center of L. 2-step nilpotent Lie algebras are useful in the study of some geometric problems, and their classification has been an important problem in Lie theory. In this paper, we give a classification of 2-step nilpotent Lie algebras of dimension 9 with 2-dimensional center. 相似文献
16.
Zhao Qiang 《Proceedings of the American Mathematical Society》1996,124(8):2501-2512
In the paper, the stability of totally geodesic submanfolds in the complex quadratic hypersurfaces: is discussed, and the indices, the nullities and the Killing nullities of totally geodesic submanifolds in are calculated.
17.
Let G be a 2-step stratified group of topological dimension d and homogeneous dimension Q. Let \({\mathcal{L}}\) be a homogeneous sub-Laplacian on G. By a theorem due to Christ and to Mauceri and Meda, an operator of the form \({F(\mathcal{L})}\) is of weak type (1, 1) and bounded on L p (G) for all p ∈ (1, ∞) whenever the multiplier F satisfies a scale-invariant smoothness condition of order s > Q/2. It is known that, for several 2-step groups and sub-Laplacians, the threshold Q/2 in the smoothness condition is not sharp and in many cases it is possible to push it down to d/2. Here we show that, for all 2-step groups and sub-Laplacians, the sharp threshold is strictly less than Q/2, but not less than d/2. 相似文献
18.
G Santhanam 《Proceedings Mathematical Sciences》1990,100(1):57-64
This paper is devoted to classifying the foliations ofG with leaves of the formgKh ?1 whereG is a compact, connected and simply connected Lie group andK is a connected closed subgroup ofG such thatG/K is a rank-1 Riemannian symmetric space. In the case whenG/K=S n, the homotopy type of space of such foliations is also given. 相似文献
19.
Barbara Opozda 《Differential Geometry and its Applications》2004,21(2):173-198
All torsion-free locally homogeneous connections on 2-dimensional manifolds are described in appropriate coordinate systems. 相似文献
20.
V. Yu. Rovenskií 《Journal of Mathematical Sciences》1990,48(1):87-94
We prove a theorem on ruled surfaces that generalizes a theorem of Ferus on totally geodesic foliations. On the basis of this theorem we obtain criteria for totally geodesic submanifolds ofS
m andCP
m that generalize and complement certain results of Borisenko, Ferus, and Abe. We give an application to the geodesic differential forms defined by Dombrowski in the case of submanifolds ofS
m andCP
m.Translated from Ukrainskií Geometricheskií Sbornik, Issue 28, 1985, pp. 106–116.The author is grateful to V. A. Toponogov for posing this problem and for attention to the work and to A. A. Borisenko for helpful criticisms. 相似文献