Austere and arid properties for PF submanifolds in Hilbert spaces |
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Affiliation: | Department of Mathematics, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumyoshi-ku, Osaka 558-8585, Japan |
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Abstract: | 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. |
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Keywords: | Minimal submanifold Austere submanifold Arid submanifold PF submanifold Hilbert space |
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