  Austere submanifolds and arid submanifolds constitute respectively two
different classes of minimal submanifolds in finite dimensional Riemannian
manifolds. In this paper we introduce these two notions 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.
