منابع مشابه
On the Geometry of Cohomogeneity One Manifolds with Positive Curvature
There are very few known examples of manifolds with positive sectional curvature. Apart from the compact rank one symmetric spaces, they exist only in dimensions 24 and below and are all obtained as quotients of a compact Lie group equipped with a biinvariant metric under an isometric group action. They consist of certain homogeneous spaces in dimensions 6, 7, 12, 13 and 24 due to Berger [Be], ...
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For an n-dimensional complete connected Riemannian manifold M with sectional curvature KM ≥ 1 and diameter diam(M) > π2 , and a closed connected totally geodesic submanifold N of M , if there exist points x ∈ N and y ∈ M satisfying the distance d(x, y) > π 2 , then N is homeomorphic to a sphere. We also give a counterexample in 2-dimensional case to the following problem: let M be an ndimension...
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This Master’s thesis is a study of some of the geometric properties of Riemannian homogeneous spaces. These are Riemannian manifolds M equipped with a transitive group of isometries G, meaning that the local geometry of the manifold is the same at every point. In Section 1.3 we see that such spaces are diffeomorphic to the quotient G/K, where G is a Lie group and K is the isotropy group at the ...
متن کاملGeometry and Rank of Fibered
Recall that the rank of a finitely generated group is the minimal number of elements needed to generate it. M. White [Whi02] has proven that the injectivity radius of M is bounded above by some function of rank(π1(M)). Building on a technique that he introduced, we show that if M is a hyperbolic 3-manifold fibering over the circle with fiber Σg and rank(π1(M)) 6= 2g + 1, then the diameter of M ...
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ژورنال
عنوان ژورنال: Communications in Analysis and Geometry
سال: 2016
ISSN: 1019-8385,1944-9992
DOI: 10.4310/cag.2016.v24.n3.a3