Abstract
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.
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Hestenes, D. (2011). The Shape of Differential Geometry in Geometric Calculus. In: Dorst, L., Lasenby, J. (eds) Guide to Geometric Algebra in Practice. Springer, London. https://doi.org/10.1007/978-0-85729-811-9_19
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DOI: https://doi.org/10.1007/978-0-85729-811-9_19
Publisher Name: Springer, London
Print ISBN: 978-0-85729-810-2
Online ISBN: 978-0-85729-811-9
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