Isometries of the Hilbert Metric
- Degree Grantor:
- University of California, Santa Barbara. Mathematics
- Degree Supervisor:
- Daryl Cooper
- Place of Publication:
- [Santa Barbara, Calif.]
- Publisher:
- University of California, Santa Barbara
- Creation Date:
- 2014
- Issued Date:
- 2014
- Topics:
- Mathematics
- Genres:
- Online resources and Dissertations, Academic
- Dissertation:
- Ph.D.--University of California, Santa Barbara, 2014
- Description:
On any convex domain in Rn we can define the Hilbert metric. A projective transformation is an example of an isometry of the Hilbert metric. In this thesis we will prove that the group of projective transformations on a convex domain has at most index 2 in the group of isometries of the convex domain with its Hilbert metric. Furthermore we will give criteria for which the set of projective transformations between two convex domains is equal to the set of isometries of the Hilbert metric of these convex domains. Lastly we will show that 2-dimensional convex domains with their corresponding Hilbert metrics are isometric if and only if they are projectively equivalent.
- Physical Description:
- 1 online resource (85 pages)
- Format:
- Text
- Collection(s):
- UCSB electronic theses and dissertations
- Other Versions:
- http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:3637501
- ARK:
- ark:/48907/f3m61hcz
- ISBN:
- 9781321203127
- Catalog System Number:
- 990045116410203776
- Copyright:
- Timothy Speer, 2014
- Rights:
- In Copyright
- Copyright Holder:
- Timothy Speer
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