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Canonical connections in Riemannian and Hermitian geometry
Thesis (MSc)--Stellenbosch University, 2024.
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| Format: | Thesis |
| Language: | en_ZA en_ZA |
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Stellenbosch : Stellenbosch University
2024
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| _version_ | 1867613915087634432 |
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| access_status_str | Open Access |
| author | Sarah, Brian |
| author2 | Bartlett, Bruce |
| author_browse | Bartlett, Bruce Sarah, Brian |
| author_facet | Bartlett, Bruce Sarah, Brian |
| author_sort | Sarah, Brian |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MSc)--Stellenbosch University, 2024. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/130514 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA en_ZA |
| last_indexed | 2026-06-10T12:43:43.080Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2024 |
| publishDateRange | 2024 |
| publishDateSort | 2024 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/130514 Canonical connections in Riemannian and Hermitian geometry Sarah, Brian Bartlett, Bruce Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Intersection theory (Mathematics) Geometry, Riemannian -- Mathematical models Hermitian structures Geometry, Differential UCTD Thesis (MSc)--Stellenbosch University, 2024. ENGLISH ABSTRACT: This thesis presents explicit calculations of three naturally occurring connec- tions in Riemannian and Hermitian geometry. Namely, the Levi-Civita con- nection and the ambient connection in Riemannian geometry, and the Chern connection and the ambient connection in Hermitian geometry. Precisely, we show that the Chern connection and the ambient connection are equal on the tautological line bundle over CP¹. Next, we show that the Levi-Civita con- nection and the ambient connection are equal on the tangent bundle of the two-sphere. Finally, we compute the Chern connection on the tangent bundle of the two-sphere regarded as a Hermitian holomorphic line bundle and show that it is equal to the Levi-Civita connection on the tangent bundle of the two-sphere. AFRIKAANSE OPSOMMING: Hierdie tesis bied eksplisiete berekeninge van drie natuurlik voorkomende ver- bindings in Riemanniaanse en Hermitiese meetkunde aan. Dit sluit die Levi- Civita-verbinding en die omgewingsverbinding in Riemanniaanse meetkunde in, sowel as die Chern-verbinding en die omgewingsverbinding in Hermitiese meetkunde. Presies, ons toon aan dat die Chern-verbinding en die omgewings- verbinding gelyk is op die tautologiese lynbundel oor CP¹. Volgende toon ons aan dat die Levi-Civita-verbinding en die omgewingsverbinding gelyk is op die raaklynbundel van die twee-sfeer. Laastens bereken ons die Chern-verbinding op die raaklynbundel van die twee-sfeer beskou as ’n Hermitiese holomorfe lynbundel en wys aan dat dit gelyk is aan die Levi-Civita-verbinding op die raaklynbundel van die twee-sfeer. Masters 2024-02-26T14:25:34Z 2024-04-26T20:22:59Z 2024-02-26T14:25:34Z 2024-04-26T20:22:59Z 2024-03 Thesis https://scholar.sun.ac.za/handle/10019.1/130514 en_ZA en_ZA Stellenbosch University application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Intersection theory (Mathematics) Geometry, Riemannian -- Mathematical models Hermitian structures Geometry, Differential UCTD Sarah, Brian Canonical connections in Riemannian and Hermitian geometry |
| title | Canonical connections in Riemannian and Hermitian geometry |
| title_full | Canonical connections in Riemannian and Hermitian geometry |
| title_fullStr | Canonical connections in Riemannian and Hermitian geometry |
| title_full_unstemmed | Canonical connections in Riemannian and Hermitian geometry |
| title_short | Canonical connections in Riemannian and Hermitian geometry |
| title_sort | canonical connections in riemannian and hermitian geometry |
| topic | Intersection theory (Mathematics) Geometry, Riemannian -- Mathematical models Hermitian structures Geometry, Differential UCTD |
| url | https://scholar.sun.ac.za/handle/10019.1/130514 |
| work_keys_str_mv | AT sarahbrian canonicalconnectionsinriemannianandhermitiangeometry |