The classification of naturally reductive homogeneous spaces in dimension 7 and 8
Die Klassifizierung natürlich reduktiver homogener Räume in den Dimensionen 7 und 8
Reinier
Storm
connection
Differential Geometry
homogeneous space
naturally reductive spaces,
Lie algebra
Mathematics
Mathematik
Mathematics
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.
Philipps-Universität Marburg
Marburg
Deutschhausstraße 9, 35037 Marburg
Ilka
Agricola
Prof.
2017
2017-04-28
2017-08-09
2017-08-10
Text
doctoralThesis
urn:nbn:de:hebis:04-z2017-05121
eng
thesis.doctoral
Philipps-Universität Marburg
Marburg
1
https://archiv.ub.uni-marburg.de/diss/z2017/0512/pdf/drws.pdf
10.17192/z2017.0512
https://archiv.ub.uni-marburg.de/diss/z2017/0512