PMATH 868Connections and Riemannian Geometry

Units: 0.50
Level: Graduate
Faculty: Mathematics
Subject: Pure Mathematics

PMATH 868 as listed in the Winter 2026 Graduate Calendar. The main page has the current version, when it runs, and seats.

Review of smooth manifolds. Vector bundles. Connections and curvature, holonomy, characteristic classes. Connections on tangent bundle: torsion, geodesics, exponential map. Riemannian geometry: Levi-Civita connection, Riemannian geodesics, Hopf-Rinow Theorem. Additional topics if time permits.

Prerequisites

Must have completed the following:
- PMATH665 - Smooth Manifolds (0.50)

Antirequisites

None listed.

Leads to

No course lists it as a requisite.

Check it elsewhere for Winter 2026

Graduate Calendar, Winter 2026The archived entry
Requirements for Winter 2026Waterloo’s requisite checker
Course outlinesSyllabi from past terms (UW login)
UW FlowStudent ratings and reviews
WClassesPast sections back to 2004, and who taught them

Calendar versions

Graduate Calendar

Older Graduate Calendars

In 11 terms, Fall 2020 to Winter 2024