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PMATH 868Connections and Riemannian Geometry

Units
0.50
Level
Graduate
Faculty
Mathematics
Subject
Pure Mathematics

When it runs

  1. F24
  2. W25
  3. S25
  4. F25
  5. W26
  6. S26
  7. F26
  8. W27
  9. S27

Ran in 2 of the last 7 terms. Winter 2027: scheduled, 1 lecture section. Spring 2027: schedule not out yet.

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. Students are expected to have background in smooth manifolds covering the topics of PMATH 665.

Prerequisites

None listed.

Antirequisites

None listed.

Leads to

No course lists it as a requisite.

Winter 2027 sections

Enrolment from UW Open Data, which can trail Quest by up to two days. Instructors and rooms: Schedule of Classes.
SectionClassEnrolledMeets
LEC 00160610 / 30TTh 08:30–09:50

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Reviewed on UW Flow

100% liked it100% easy100% useful

From 1 rating and 1 comment on UW Flow. The most helpful comments, quoted as written, without names. Read them all on UW Flow.

  • started with a lot of general theory of fibre bundles and vector bundles, before covering connections, their induced exterior covariant derivatives, the basics of riemannian geometry, then ended with parallel transport, holonomy, and characteristic classes. It felt like the presentation could've been a lot cleaner and more streamlined, as well as a bit more careful in some spots (what holds locally vs globally, and the notation was consistently terrible). though as always Ruxandra is extremely nice and willing to help you understand. essential if you care about geometry

    Apr 2025 · liked itOn UW FlowRemove this

Discussed on r/uwaterloo

One post or comment in 1 thread mentions PMATH 868, July 2023 to December 2024. Quoted word for word, newest first; each reply sits under the post and the comment that started its branch. Search r/uwaterloo for newer posts.

Spring 2023

Check it elsewhere for Fall 2026

Calendar versions

Graduate Calendar

Older Graduate Calendars

In 11 terms, Fall 2020 to Winter 2024