Grove--Shiohama type sphere theorem in Finsler geometry
Grove--Shiohama type sphere theorem in Finsler geometry
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Grove--芬斯勒几何中的盐浜型球面定理
DOI：
10.18910/57686
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发表时间：
2013
影响因子：
0.4
通讯作者：
K. Kondo
中科院分区：
文献类型：
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作者：
K. Kondo
本文从径向曲率几何的观点出发，证明了某些紧致Finsler流形的Grove-Shiohama型球面定理。毫无疑问，整体黎曼几何中最美丽的定理之一是Grove和Shiohama的直径球定理[GS]。在他们的证明中，Toponogov的比较定理与他们自己介绍的距离函数的临界点理论一起被非常认真地应用fi。也就是说，如果完备黎曼流形X有一个临界点，即距离函数dp到点p∈X的临界点Q∈X，则Q是p的截点。因此，dp在Q处不是可除的(ff)。然而，他们克服了分析障碍，将原始的TCT应用于内角为∠(Pxy)≤π/2的三角形(Pxy)。本文的目的是证明一类正向完备Finsler流形的Grove-Shiohama型球面定理，这类流形的径向flAg曲率由下有界
AbstractFrom radial curvature geometry’s standpoint, we prove a few sphere theoremsof the Grove-Shiohama type for certain classes of compact Finsler manifolds. 1 Introduction Beyond a doubt, one of the most beautiful theorems in global Riemannian geometry isthe diameter sphere theorem of Grove and Shiohama [GS]. In their proof, Toponogov’scomparison theorem (TCT) was very first applied seriously together with the critical pointtheory, introduced by themselves, of distance functions. That is, if a complete Riemannianmanifold X has a critical point, say q ∈ X \ {p} , of the distance function d p to a point p ∈ X , then q is the cut point of p . And hence d p is not differentiable at q . However, theyovercame the analytical obstruction by applying the original TCT to the triangle △ ( pxy )with the interior angle ∠( pxy ) ≤ π/ 2 at x . That is the point, i.e., they took the manifoldinto their hands by directly drawing segments on it.Our purpose of this article is to prove a sphere theorem of the Grove-Shiohama typefor a certain class of forward complete Finsler manifolds whose radial flag curvatures arebounded below by
DOI：
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发表时间：
2009
期刊：
影响因子：
--
作者：
T. Hamada;K. Shiohama;K.Nakamoto and T.Torii;堀内澄子;塩濱勝博
通讯作者：
塩濱勝博
DOI：
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发表时间：
--
期刊：
Geometric and Functional Analysis (掲載決定)
影响因子：
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作者：
Kei Kondo;Shin-ichi Ohta
通讯作者：
Shin-ichi Ohta