## Differential Geometry of Curves and SurfacesThis volume covers local as well as global differential geometry of curves and surfaces. |

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#### Review: Differential Geometry of Curves and Surfaces

User Review - Mark Hoyle - GoodreadsExcellent treatise on curves and surfaces with very clear exposition of the motivation behind many concepts in Riemannian Geometry. Read full review

### Contents

Regular Surfaces | 51 |

and Differentiability | 118 |

The Intrinsic Geometry of Surfaces | 217 |

Copyright | |

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### Common terms and phrases

angle apply arc length Assume asymptotic axis basis bounded called choose circle closed compact complete compute conclude condition connected consider const constant contained continuous contradiction converges coordinate neighborhood covering curvature curve cylinder defined definition denote depend derivative determined diffeomorphism differentiable differentiable function direction equal equations Example Exercise exists expression extended fact Figure follows function fundamental form Gaussian curvature geodesic geometry give given hence homeomorphism integral intersection interval isometry joining Lemma linear locally means minimal neighborhood Observe obtain open set orientation orthogonal parallel parametrized parametrized curve passing plane positive possible proof Prop PROPOSITION prove region regular surface relation Remark respectively restriction satisfies segment sequence Show simple sphere tangent plane tangent vector theorem unique unit variation vector field zero