Browsing by Author "Sarah, Brian"

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    Canonical connections in Riemannian and Hermitian geometry
    (Stellenbosch : Stellenbosch University, 2024-03) Sarah, Brian; Bartlett, Bruce; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences.
    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.