The Isometry Groups of Manifolds and the Automorphism Groups of Domains

Abstract

ABSTRACT. We prove that every compact Lie group can be realized as the (full) automorphism group of a strictly pseudoconvex domain and as the (full) isometry group of a compact, connected, smooth Riemannian manifold.

Realizing connected Lie groups as automorphism groups of complex manifolds

“…(4) In the real-analytic category, W does not need to be smooth, it suffices if W is a (possibly singular) real-analytic subset. As explained in [13], this can be verified using the fact that a real analytic subset W admits a stratification…”

“…Once this has been verified, we can prove (using arguments similar to those used in [13], [2]) that φ extends as holomorphic map near lim(x n ), and use the theory of Chern-Moser-invariants to deduce that φ was in fact given by left multiplication with an element of G. Vol. 79 (2004) Connected Lie groups as automorphism groups 287…”

Aspects of Differential Geometry II

“…We refer to Myers and Steenrod [45] and to Palais [50] for the proof of Assertion 1, and to Saerens and Zame [55] for the proof of Assertion 2 as these results are beyond the scope of this book. ; Á/ D .…”

Prescribed Riemannian Symmetries

“…As for Question 1.1, Corollary 4.4 below recovers that affirmative answer for connected compact Lie groups. There are trade-offs as compared to [3,Theorem 3] and [32,Theorem 1]: while the latter make no connectedness assumptions, the Riemannian manifolds obtained here (with prescribed symmetry group) tend to have smaller dimension.…”