Canonical connections in Riemannian and Hermitian geometry

Simple item page
dc.contributor.advisorBartlett, Bruceen_ZA
dc.contributor.authorSarah, Brianen_ZA
dc.contributor.otherStellenbosch University. Faculty of Science. Dept. of Mathematical Sciences.en_ZA
dc.date.accessioned2024-02-26T14:25:34Z
dc.date.accessioned2024-04-26T20:22:59Z
dc.date.available2024-02-26T14:25:34Z
dc.date.available2024-04-26T20:22:59Z
dc.date.issued2024-03
dc.descriptionThesis (MSc)--Stellenbosch University, 2024. en_ZA
dc.description.abstractENGLISH 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.en_ZA
dc.description.abstractAFRIKAANSE 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.af_ZA
dc.description.versionMastersen_ZA
dc.identifier.urihttps://scholar.sun.ac.za/handle/10019.1/130514
dc.language.isoen_ZAen_ZA
dc.language.isoen_ZAen_ZA
dc.publisherStellenbosch : Stellenbosch Universityen_ZA
dc.rights.holderStellenbosch Universityen_ZA
dc.subject.lcshIntersection theory (Mathematics)en_ZA
dc.subject.lcshGeometry, Riemannian -- Mathematical modelsen_ZA
dc.subject.lcshHermitian structuresen_ZA
dc.subject.lcshGeometry, Differentialen_ZA
dc.subject.nameUCTDen_ZA
dc.titleCanonical connections in Riemannian and Hermitian geometryen_ZA
dc.typeThesisen_ZA
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
sarah_canonical_2024.pdf
Size:
1022.24 KB
Format:
Adobe Portable Document Format
Description:
Download
Collections
Masters Degrees (Mathematical Sciences)