TY - JOUR

T1 - Induction of Geometric Actions

AU - Adams, Scot

PY - 2001/12/1

Y1 - 2001/12/1

N2 - We prove that, in some situations, an induced action from a normal subgroup preserves a geometric structure. Combined with known geometric rigidity results, this result implies certain rigidity statements concerning the full diffeomorphism group of a manifold. It also provides many examples of actions on Lorentz manifolds. Combining these with a small number of well-known actions, we get the full list of connected, simply connected Lie groups admitting a locally faithful, orbit nonproper action by isometrics of a connected Lorentz manifold. We give an example of a connected nilpotent Lie group with no complicated action on a Lorentz manifold. We show that, if a connected Lie group has a normal closed subgroup isomorphic to a (two-dimensional) cylinder, then it admits a locally faithful, orbit nonproper action by isometrics of a connected Lorentz manifold.

AB - We prove that, in some situations, an induced action from a normal subgroup preserves a geometric structure. Combined with known geometric rigidity results, this result implies certain rigidity statements concerning the full diffeomorphism group of a manifold. It also provides many examples of actions on Lorentz manifolds. Combining these with a small number of well-known actions, we get the full list of connected, simply connected Lie groups admitting a locally faithful, orbit nonproper action by isometrics of a connected Lorentz manifold. We give an example of a connected nilpotent Lie group with no complicated action on a Lorentz manifold. We show that, if a connected Lie group has a normal closed subgroup isomorphic to a (two-dimensional) cylinder, then it admits a locally faithful, orbit nonproper action by isometrics of a connected Lorentz manifold.

KW - Isometrics

KW - Lorentz manifolds

KW - Transformation groups

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U2 - 10.1023/A:1013191613349

DO - 10.1023/A:1013191613349

M3 - Article

AN - SCOPUS:0007410164

VL - 88

SP - 91

EP - 112

JO - Geometriae Dedicata

JF - Geometriae Dedicata

SN - 0046-5755

IS - 1-3

ER -