The Shape of Differential Geometry in Geometric Calculus

  • David Hestenes


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.


Differential Geometry Tangent Space Tangent Vector Fundamental Theorem Tangent Cone 
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© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Arizona State UniversityTempeUSA

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