共查询到20条相似文献,搜索用时 31 毫秒
1.
Giovanni Calvaruso 《Differential Geometry and its Applications》2008,26(4):419-433
We study three-dimensional pseudo-Riemannian manifolds having distinct constant principal Ricci curvatures. These spaces are described via a system of differential equations, and a simple characterization is proved to hold for the locally homogeneous ones. We then generalize the technique used in [O. Kowalski, F. Prüfer, On Riemannian 3-manifolds with distinct constant Ricci eigenvalues, Math. Ann. 300 (1994) 17-28] for Riemannian manifolds and construct explicitly homogeneous and non-homogeneous pseudo-Riemannian metrics in R3, having the prescribed principal Ricci curvatures. 相似文献
2.
T. Arias-Marco 《Differential Geometry and its Applications》2007,25(1):29-34
In this short note we correct the (incomplete) classification theorem from [F. Podestà, A. Spiro, Four-dimensional Einstein-like manifolds and curvature homogeneity, Geom. Dedicata 54 (1995) 225-243], we improve a result from [P. Bueken, L. Vanhecke, Three- and four-dimensional Einstein-like manifolds and homogeneity, Geom. Dedicata 75 (1999) 123-136] and we announce the final solution of the classification problem for 4-dimensional homogeneous D'Atri spaces. 相似文献
3.
A classification of homogeneous pseudo-Riemannian structures and a characterization of each primitive class are obtained. Several examples are also given. 相似文献
4.
The aim of this paper is to classify 4-dimensional Einstein-like manifolds whose Ricci tensor has constant eigenvalues (this being a special kind of curvature homogeneity condition). We give a full classification when the Ricci tensor is of Codazzi type; when the Ricci tensor is cyclic parallel, we classify all such manifolds when not all Ricci curvatures are distinct. In this second case we find a one-parameter family of Riemannian metrics on a Lie groupG as the only possible ones which are irreducible and non-symmetric. 相似文献
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We present some examples of curvature homogeneous pseudo-Riemannian manifolds
which are k-spacelike Jordan Stanilov. 相似文献
7.
Giovanni Calvaruso 《Differential Geometry and its Applications》2011,29(6):758-769
We obtain the full classification of invariant symplectic, (almost) complex and Kähler structures, together with their paracomplex analogues, on four-dimensional pseudo-Riemannian generalized symmetric spaces. We also apply these results to build some new examples of five-dimensional homogeneous K-contact, Sasakian, K-paracontact and para-Sasakian manifolds. 相似文献
8.
J. Carlos Díaz-Ramos Eduardo García-Río Lieven Vanhecke 《Monatshefte für Mathematik》2006,149(4):303-322
We study some scalar curvature invariants on geodesic spheres and use them to characterize several kinds of Riemannian manifolds
such as homogenous manifolds and in particular, the two-point homogeneous spaces and the Damek-Ricci spaces. 相似文献
9.
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
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I. G. Nikolaev 《Commentarii Mathematici Helvetici》1995,70(1):210-234
Schur's theorem states that an isotropic Riemannian manifold of dimension greater than two has constant curvature. It is natural
to guess that compact almost isotropic Riemannian manifolds of dimension greater than two are close to spaces of almost constant
curvature. We take the curvature anisotropy as the discrepancy of the sectional curvatures at a point. The main result of
this paper is that Riemannian manifolds in Cheeger's class ℜ(n,d,V,A) withL
1-small integral anisotropy haveL
p-small change of the sectional curvature over the manifold. We also estimate the deviation of the metric tensor from that
of constant curvature in theW
p
2
-norm, and prove that compact almost isotropic spaces inherit the differential structure of a space form. These stability
results are based on the generalization of Schur' theorem to metric spaces. 相似文献
12.
Flat pseudo-Riemannian manifolds with a nilpotent transitive group of isometries are shown to be complete. Also flat pseudo-Riemannian homogeneous manifolds with non-trivial holonomy are shown to contain a complete geodesic. 相似文献
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16.
V.N. Berestovski? 《Differential Geometry and its Applications》2011,29(4):533-546
The authors give a short survey of previous results on generalized normal homogeneous (δ-homogeneous, in other terms) Riemannian manifolds, forming a new proper subclass of geodesic orbit spaces with nonnegative sectional curvature, which properly includes the class of all normal homogeneous Riemannian manifolds. As a continuation and an application of these results, they prove that the family of all compact simply connected indecomposable generalized normal homogeneous Riemannian manifolds with positive Euler characteristic, which are not normal homogeneous, consists exactly of all generalized flag manifolds Sp(l)/U(1)⋅Sp(l−1)=CP2l−1, l?2, supplied with invariant Riemannian metrics of positive sectional curvature with the pinching constants (the ratio of the minimal sectional curvature to the maximal one) in the open interval (1/16,1/4). This implies very unusual geometric properties of the adjoint representation of Sp(l), l?2. Some unsolved questions are suggested. 相似文献
17.
Fabio Podestà 《Monatshefte für Mathematik》1996,122(3):215-225
This work deals with positively curved compact Riemannian manifolds which are acted on by a closed Lie group of isometries whose principal orbits have codimension one and are isotropy irreducible homogeneous spaces. For such manifolds we can show that their universal covering manifold may be isometrically immersed as a hypersurface of revolution in an euclidean space. 相似文献
18.
Bang-Yen Chen 《Central European Journal of Mathematics》2009,7(3):400-428
Submanifolds with parallel mean curvature vector play important roles in differential geometry, theory of harmonic maps as
well as in physics. Spatial surfaces in 4D Lorentzian space forms with parallel mean curvature vector were classified by B.
Y. Chen and J. Van der Veken in [9]. Recently, spatial surfaces with parallel mean curvature vector in arbitrary pseudo-Euclidean
spaces are also classified in [7]. In this article, we classify spatial surfaces with parallel mean curvature vector in pseudo-Riemannian
spheres and pseudo-hyperbolic spaces with arbitrary codimension and arbitrary index. Consequently, we achieve the complete
classification of spatial surfaces with parallel mean curvature vector in all pseudo-Riemannian space forms. As an immediate
by-product, we obtain the complete classifications of spatial surfaces with parallel mean curvature vector in arbitrary Lorentzian
space forms.
相似文献
19.
A Riemannian g.o. manifold is a homogeneous Riemannian manifold (M,g) on which every geodesic is an orbit of a one-parameter group of isometries. It is known that every simply connected Riemannian g.o. manifold of dimension ?5 is naturally reductive. In dimension 6 there are simply connected Riemannian g.o. manifolds which are in no way naturally reductive, and their full classification is known (including compact examples). In dimension 7, just one new example has been known up to now (namely, a Riemannian nilmanifold constructed by C. Gordon). In the present paper we describe compact irreducible 7-dimensional Riemannian g.o. manifolds (together with their “noncompact duals”) which are in no way naturally reductive. 相似文献
20.
Claudio Arezzo 《Advances in Mathematics》2005,191(1):209-223
In this paper we show the existence of stable symplectic non-holomorphic two-spheres in Kähler manifolds of positive constant scalar curvature of real dimension four and in Kähler-Einstein Fano manifolds of real dimension six. Some of the techniques used involve deformation theory of algebraic cycles. 相似文献