منابع مشابه
Simplicial Nonpositive Curvature
We introduce a family of conditions on a simplicial complex that we call local klargeness (k ≥ 6 is an integer). They are simply stated, combinatorial and easily checkable. One of our themes is that local 6-largeness is a good analogue of the nonpositive curvature: locally 6-large spaces have many properties similar to nonpositively curved ones. However, local 6-largeness neither implies nor is...
متن کاملNonpositive curvature of blow - ups
Consider the following situation: MC is a complex manifold of complex dimension n, and DC is a union of smooth complex codimension-one submanifolds (i.e., DC is a smooth divisor). Examples of this situation include: (1) arrangements of projective hyperplanes in CP, as well as various blow-ups of such arrangements along intersections of hyperplanes, (2) nonsingular toric varieties (whereDC is th...
متن کاملNonpositive Curvature and Reflection Groups
Introduction. A space is aspherical if its universal cover is contractible. Examples of aspherical spaces occur in differential geometry (as complete Riemannian manifolds of nonpositive sectional curvature), in Lie groups (as Γ\G/K where G is a Lie group, K is a maximal compact subgroup and Γ is a discrete torsion-free subgroup), in 3-manifold theory and as certain 2-dimensional cell complexes....
متن کاملGeodesic Flows in Manifolds of Nonpositive Curvature
I. Introduction-a quick historical survey of geodesic flows on negatively curved spaces. II. Preliminaries on Riemannian manifolds A. Riemannian metric and Riemannian volume element B. Levi Civita connection and covariant differentiation along curves C. Parallel translation of vectors along curves D. Curvature E. Geodesics and geodesic flow F. Riemannian exponential map and Jacobi vector fields...
متن کاملFinsler Manifolds with Nonpositive Flag Curvature and Constant S-curvature
The flag curvature is a natural extension of the sectional curvature in Riemannian geometry, and the S-curvature is a non-Riemannian quantity which vanishes for Riemannian metrics. There are (incomplete) nonRiemannian Finsler metrics on an open subset in Rn with negative flag curvature and constant S-curvature. In this paper, we are going to show a global rigidity theorem that every Finsler met...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2009
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2009.03.036