Principal Curvatures: Gaussian Curvature

This lecture covers the concept of principal curvatures and Gaussian curvature in the context of minimal surfaces. Starting with the definition of mean curvature, the instructor explains how to calculate the Gaussian curvature and its significance in determining minimal surfaces. Through examples like the helicoid, the lecture demonstrates the application of these concepts in real-world scenarios. The discussion also includes the calculation of principal curvatures and the roots of the characteristic polynomial. The session concludes with a preview of the upcoming topic on Gaussian curvature applications.