Guide to Geometric Algebra in Practice

pp 393-410

The Shape of Differential Geometry in Geometric Calculus

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We review the foundations for coordinate-free differential geometry in Geometric Calculus. In particular, we see how both extrinsic and intrinsic geometry of a manifold can be characterized by a single bivector-valued one-form called the Shape Operator. The challenge is to adapt this formalism to Conformal Geometric Algebra for wide application in computer science and engineering.