Indefinite extrinsic symmetric spaces II
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Ines Kath
Abstract
Having developed a description of indefinite extrinsic symmetric spaces by corresponding infinitesimal objects in the preceding paper we now study the classification problem for these algebraic objects. In most cases the transvection group of an indefinite extrinsic symmetric space is not semisimple, which makes the classification difficult. We use the recently developed method of quadratic extensions for (𝔥, K)-invariant metric Lie algebras to tackle this problem. We obtain a one-to-one correspondence between isometry classes of extrinsic symmetric spaces and a certain cohomology set. This allows a systematic construction of extrinsic symmetric spaces and explicit classification results, e.g., if the metric of the embedded manifold or the ambient space has a small index. We will illustrate this by classifying all Lorentzian extrinsic symmetric spaces.
©[2012] by Walter de Gruyter Berlin Boston
Articles in the same Issue
- Evolution families and the Loewner equation I: the unit disc
- Minimally invasive surgery for Ricci flow singularities
- Indefinite extrinsic symmetric spaces II
- A parabolic flow toward solutions of the optimal transportation problem on domains with boundary
- A proof of Subbarao's conjecture
- Regularized theta lifts for orthogonal groups over totally real fields
- Approximation properties for free orthogonal and free unitary quantum groups
Articles in the same Issue
- Evolution families and the Loewner equation I: the unit disc
- Minimally invasive surgery for Ricci flow singularities
- Indefinite extrinsic symmetric spaces II
- A parabolic flow toward solutions of the optimal transportation problem on domains with boundary
- A proof of Subbarao's conjecture
- Regularized theta lifts for orthogonal groups over totally real fields
- Approximation properties for free orthogonal and free unitary quantum groups
