10.17192/z2017.0512
Storm, Reinier
Reinier
Storm
The classification of naturally reductive homogeneous spaces in dimension 7 and 8
Die Klassifizierung natürlich reduktiver homogener Räume in den Dimensionen 7 und 8
Philipps-Universität Marburg
2017
connection
Differential Geometry
homogeneous space
naturally reductive spaces,
Geometrie
Lie algebra
Algebra
Klassifikation
Mathematics
Mathematik
Mathematik
Mathematics
Mathematik und Informatik
Agricola, Ilka (Prof.)
2017-08-10
2017-08-09
en
DoctoralThesis
https://archiv.ub.uni-marburg.de/diss/z2017/0512
urn:nbn:de:hebis:04-z2017-05121
//archiv.ub.uni-marburg.de/diss/z2017/0512/cover.png
application/pdf
https://rightsstatements.org/vocab/InC-NC/1.0/
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.