## A New Approach to Differential Geometry using Clifford's Geometric AlgebraDifferential geometry is the study of the curvature and calculus of curves and surfaces. The conceptual complications introduced by a multitude of spaces and mappings normally required in the study of differential geometry usually postpones the topic to graduate-level courses.
Key features include:
· a rare undergraduate-level approach to differential geometry; · brief biographies of historically relevant mathematicians and physicists; · significant aspects of general relativity and Riemannian geometry and · chapter-by-chapter exercises.
This accessible and comprehensive textbook offers a valuable introduction to differential geometry, simplifying the complicated theory by using Clifford algebra. It will serve as a useful resource for upper-level undergraduates, beginning-level graduate students, and researchers in the algebra and physics communities.
This accessible and comprehensive textbook offers a valuable introduction to differential geometry, simplifying the complicated theory by using Clifford algebra. It will serve as a useful resource for upper-level undergraduates, beginning-level graduate students, and researchers in the algebra and physics communities. |

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### Contents

Chapter 1 Introduction | 1 |

Chapter 2 Clifford Algebra in Euclidean 3Space | 3 |

Chapter 3 Clifford Algebra in Minkowski 4Space | 27 |

Chapter 4 Clifford Algebra in Flat nSpace | 47 |

Chapter 5 Curved Spaces | 121 |

Chapter 6 The GaussBonnet Formula | 181 |

Chapter 7 Some Extrinsic Geometry in En | 227 |

Chapter 8 NonEuclidean Hyperbolic Geometry | 299 |

Chapter 11 Minimal Surfaces | 375 |

Chapter 12 Some General Relativity | 395 |

Chapter A A Matrix Representation of a Clifford Algebra | 431 |

Chapter B Construction of Matrix Representations for Dirac Vectors | 436 |

Chapter C A Few Terms of the Taylors Series for the UrdıCopernican Model for the Outer Planets | 441 |

Chapter D A Few Terms of the Taylors Series for Keplers Orbits | 444 |

449 | |

459 | |

### Other editions - View all

A New Approach to Differential Geometry using Clifford's Geometric Algebra John Snygg Limited preview - 2011 |