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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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| Định dạng: | Dissertation |
| Ngôn ngữ: | Tiếng Anh |
| Được phát hành: |
Philipps-Universität Marburg
2017
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| Những chủ đề: | |
| Truy cập trực tuyến: | Bài toàn văn PDF |
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| Tóm tắt: | 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. |
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| DOI: | 10.17192/z2017.0512 |