The classification of naturally reductive homogeneous spaces in dimension 7 and 8

Naturally reductive spaces are studied with the aim to classify them. The in this thesis developed theory contains a construction which produces many unknown non-normal homogeneous naturally reductive spaces. It is proved that this construction exhausts all naturally re...

Ausführliche Beschreibung

Gespeichert in:
1. Verfasser: Storm, Reinier
Beteiligte: Agricola, Ilka (Prof.) (BetreuerIn (Doktorarbeit))
Format: Dissertation
Sprache:Englisch
Veröffentlicht: Philipps-Universität Marburg 2017
Mathematik und Informatik
Ausgabe:http://dx.doi.org/10.17192/z2017.0512
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Zusammenfassung:Naturally reductive spaces are studied with the aim to classify them. The in this thesis developed theory contains a construction which produces many unknown non-normal homogeneous naturally reductive spaces. It is proved that this construction exhausts all naturally reductive spaces. This makes it possible to describe all spaces in a uniform way. In this framework the isomorphism problem can be solved, i.e. decide when two given naturally reductive structures are isomorphic. Similarly the reducibility problem is dealt with. This theory is also excellent for classifying naturally reductive spaces. This is explicitly done in dimension 7 and 8.
DOI:http://dx.doi.org/10.17192/z2017.0512