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

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 reductive spaces. This makes it...

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Bibliographische Detailangaben
1. Verfasser: Storm, Reinier
Beteiligte: Agricola, Ilka (Prof.) (BetreuerIn (Doktorarbeit))
Format: Dissertation
Sprache:Englisch
Veröffentlicht: Philipps-Universität Marburg 2017
Schlagworte:
Mathematik
Klassifikation
homogeneous space
Algebra
Differential Geometry
Geometrie
naturally reductive spaces,
connection
Lie algebra
Mathematics
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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:10.17192/z2017.0512

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