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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.
Anca-Iuliana Bonciocat 《Journal of Functional Analysis》2009,256(9):2944-2292
We introduce and study rough (approximate) lower curvature bounds for discrete spaces and for graphs. This notion agrees with the one introduced in [J. Lott, C. Villani, Ricci curvature for metric-measure spaces via optimal transport, Ann. of Math. 169 (2009), in press] and [K.T. Sturm, On the geometry of metric measure spaces. I, Acta Math. 196 (2006) 65-131], in the sense that the metric measure space which is approximated by a sequence of discrete spaces with rough curvature ?K will have curvature ?K in the sense of [J. Lott, C. Villani, Ricci curvature for metric-measure spaces via optimal transport, Ann. of Math. 169 (2009), in press; K.T. Sturm, On the geometry of metric measure spaces. I, Acta Math. 196 (2006) 65-131]. Moreover, in the converse direction, discretizations of metric measure spaces with curvature ?K will have rough curvature ?K. We apply our results to concrete examples of homogeneous planar graphs. 相似文献
3.
Let H be a closed, connected subgroup of a connected, simple Lie group G with finite center. The homogeneous space G/H has a tessellation if there is a discrete subgroup of G, such that acts properly discontinuously on G/H, and the double-coset space \G/H is compact. Note that if either H or G/H is compact, then G/H has a tessellation; these are the obvious examples.It is not difficult to see that if G has real rank one, then only the obvious homogeneous spaces have tessellations. Thus, the first interesting case is when G has real rank two. In particular, Kulkarni and Kobayashi constructed examples that are not obvious when G=SO(2, 2n)° or SU(2, 2n). Oh and Witte constructed additional examples in both of these cases, and obtained a complete classification when G=SO(2, 2n)°. We simplify the work of Oh-Witte, and extend it to obtain a complete classification when G=SU(2, 2n). This includes the construction of another family of examples.The main results are obtained from methods of Benoist and Kobayashi: we fix a Cartan decomposition G=K
A
+
K, and study the intersection (K
H
K)A
+. Our exposition generally assumes only the standard theory of connected Lie groups, although basic properties of real algebraic groups are sometimes also employed; the specialized techniques that we use are developed from a fairly elementary level. 相似文献
4.
Dragan S. Djordjevi 《Journal of Computational and Applied Mathematics》2007,200(2):701-704
In this paper we find the explicit solution of the equation
A*X+X*A=B