Austere and arid properties for PF submanifolds in Hilbert spaces
Austere and arid properties for PF submanifolds in Hilbert spaces
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希尔伯特空间中 PF 子流形的严峻和干旱性质
DOI：
10.1016/j.difgeo.2020.101613
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发表时间：
2020
影响因子：
0.5
通讯作者：
Masahiro Morimoto
中科院分区：
文献类型：
--
作者：
Miyamoto Kou;She Jinhua;Sato Daiki;Masahiro Morimoto;Masahiro Morimoto
有限维黎曼流形中的严格子流形和粗糙子流形分别构成两类不同的极小子流形。本文将这些子流形的概念引入到Hilbert空间中的一类真Fredholm（PF）子流形中，讨论了它们之间的关系，并给出了Hilbert空间中无限维严格PF子流形和干旱PF子流形的例子。我们还提到了Hilbert空间上超极PF作用中极小轨道的分类问题。
Austere submanifolds and arid submanifolds constitute respectively two different classes of minimal submanifolds in finite dimensional Riemannian manifolds. In this paper we introduce the concepts of these submanifolds into a class of proper Fredholm (PF) submanifolds in Hilbert spaces, discuss their relation and show examples of infinite dimensional austere PF submanifolds and arid PF submanifolds in Hilbert spaces. We also mention a classification problem of minimal orbits in hyperpolar PF actions on Hilbert spaces.