Lie-Einstein Spaces in Low Dimensions
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University of Toledo / OhioLINK
2018
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ndltd-OhioLink-oai-etd.ohiolink.edu-toledo15332059219684662021-08-03T07:07:54Z Lie-Einstein Spaces in Low Dimensions Subedi, Rishi R. Mathematics A Lie-Einstein space is an invariant Riemannian metric on a Lie group such thatthe Ricci tensor is multiple of the metric. This dissertation concerns Lie-Einsteinspaces of in dimensions five and six. In dimension five we attempt to solve theproblem in general, that is without making any assumptions about the form of themetric. Partial results are found. In dimension six we consider solvable Lie groups.Since the conditions are already very complicated in dimension five, we make theassumptions that the metric is of diagonal form in the invariant Lie algebra basis forcodimension one nilradical algebras classified by Mubarakzyanov. We also restrictattention to those algebras where the adjoint matrix of the basis element not inthe nilradical is semi-simple. In the case of the Turkowski algebras, that have acodimension two nilradical, we assume that the metric is diagonal on the nilradicaland that its complement is orthogonal to the nilradical; the Lie algebras concernedare such that the adjoint matrices of the basis elements not in the nilradical are semi-simple and commute. In all cases the conditions are checked twice, first using aninvariant Lie algebra basis. Then these results are checked again using a coordinaterepresentation of the Lie algebra basis and the associated Lie-Einstein metrics arewritten down using a basis of a coordinate presentation of the associated one-forms. 2018 English text University of Toledo / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=toledo1533205921968466 http://rave.ohiolink.edu/etdc/view?acc_num=toledo1533205921968466 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws. |
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NDLTD |
| language |
English |
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NDLTD |
| topic |
Mathematics |
| spellingShingle |
Mathematics Subedi, Rishi R. Lie-Einstein Spaces in Low Dimensions |
| author |
Subedi, Rishi R. |
| author_facet |
Subedi, Rishi R. |
| author_sort |
Subedi, Rishi R. |
| title |
Lie-Einstein Spaces in Low Dimensions |
| title_short |
Lie-Einstein Spaces in Low Dimensions |
| title_full |
Lie-Einstein Spaces in Low Dimensions |
| title_fullStr |
Lie-Einstein Spaces in Low Dimensions |
| title_full_unstemmed |
Lie-Einstein Spaces in Low Dimensions |
| title_sort |
lie-einstein spaces in low dimensions |
| publisher |
University of Toledo / OhioLINK |
| publishDate |
2018 |
| url |
http://rave.ohiolink.edu/etdc/view?acc_num=toledo1533205921968466 |
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AT subedirishir lieeinsteinspacesinlowdimensions |
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