Curvature for General Algebraic Surfaces - Differential Geometry Lecture 29

Explore the extension of curvature concepts to general algebraic surfaces in this advanced differential geometry lecture. Delve into complex formulas with elegant symmetry, starting with paraboloids and progressing to general quadrics. Learn how to compute curvatures for hypersurfaces in affine space. Examine theorems on paraboloids with vertices, special cases, and general conics. Gain insights into the powerful applications of these mathematical concepts in understanding surface geometry.

Introduction
Theorem; A paraboloid with vertex Theorem
Special case of the paraboloid with vertex
Paraboloid 0=?
Theorem
General conic through 0,00
Theorem - The General quadic
Some implications