MATH 545 Differential Geometry

This is an introduction to the study of smooth surfaces in 3-dimensional space. Topics include the shape operator on a smooth surface and its properties, principal curvatures and lines of curvature, and Gauss and mean curvature. Additional topics may include Gauss’ theorem Egregium, isometric surfaces, minimal surface theory and geodesics.




Multivariable calculus, linear algebra and at least one proof-based mathematics course