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It is known that an isometric action of a Lie group on a compact symmetricspace gives rise to a proper Fredholm action of a path group on a path spacevia the gauge transformations. In this paper, supposing that the isometricaction is a Hermann action (i.e. an isometric action of a symmetric subgroup ofthe isometry group) we give an explicit formula for the principal curvatures oforbits of the path group action and study the condition for those orbits to beaustere, that is, the set of principal curvatures in the direction of eachnormal vector is invariant under the multiplication by minus one. To prove theresults we essentially use the facts that Hermann actions are hyperpolar andall orbits of Hermann actions are curvature-adapted submanifolds. The resultsgreatly extend the author's previous result in the case of the standard sphereand show that there exist a larger number of infinite dimensional austeresubmanifolds in Hilbert spaces.

Curvatures and austere property of orbits of path group actions induced by Hermann actions