Contact Info
Pure MathematicsUniversity of Waterloo
200 University Avenue West
Waterloo, Ontario, Canada
N2L 3G1
Departmental office: MC 5304
Phone: 519 888 4567 x43484
Fax: 519 725 0160
Email: puremath@uwaterloo.ca
Last time we discussed the concrete geometric meaning of Gaussian curvature of surfaces in R3. In this talk we will use the Gaussian curvature to give geometric meaning to the sectional, Ricci and scalar curvatures of an arbitrary Riemannian manifold. To do this, we will also need to define totally geodesic submanifolds. In the case of R3, it turns out that the first and second fundamental form completely classify the surfaces. This is made precise by a theorem of Bonnet, which I will state. After doing this, we will discuss the Codazzi equations and see how they, together with the Gauss equation, are generalizations of this classification theorem for surfaces.
Please note room
Departmental office: MC 5304
Phone: 519 888 4567 x43484
Fax: 519 725 0160
Email: puremath@uwaterloo.ca
The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.