A Classification of Horizontally Homothetic Submersions from Space Forms of Nonnegative Curvature
A Classification of Horizontally Homothetic Submersions from Space Forms of Nonnegative Curvature
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非负曲率空间形式的水平拟似淹没分类
DOI：
10.1112/s0024609306018467
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发表时间：
2006
影响因子：
0.9
通讯作者：
G. Walschap
中科院分区：
文献类型：
--
作者：
Ye;G. Walschap
证明了对于n⩾2，任意水平同伦下沉φ：Rn+1→(NN，h)都是直至同伦的黎曼下沉.如果φ：Sn+1→(NN，h)是水平同调下沉，则n=2m，(NN，h)与φ等距，并且直到同伦，φ是标准的→纤维S2m+1 CPm。2000年数学科目分类53C20、53C12。
In this paper, it is proved that for n ⩾ 2, any horizontally homothetic submersion φ: Rn+1 → (Nn, h) is a Riemannian submersion up to a homothety. It is also shown that if φ: Sn+1 → (Nn, h) is a horizontally homothetic submersion, then n = 2m, (Nn, h) is isometric to CPm and, up to a homothety, φ is a standard Hopf fibration S2m+1 → CPm. 2000 Mathematics Subject Classification 53C20, 53C12.