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

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### Contents

Regular Surfaces | 51 |

and Differentiability | 118 |

The Intrinsic Geometry of Surfaces | 217 |

Copyright | |

5 other sections not shown

### Common terms and phrases

angle appendix to Chap arc length arcwise connected Assume asymptotic curves axis called closed curve coefficients compact complete surface compute condition conjugate const constant contained continuous contradiction convex coordinate curves coordinate neighborhood covariant derivative cylinder defined definition denote diffeomorphism differentiable function differentiable map differential geometry equations Example Exercise exists a neighborhood expp fact Figure follows Gauss map Gauss-Bonnet theorem Gaussian curvature geodesic given global hence homeomorphism inner product intersection isometry Jacobi field Lemma Let p e linear map lines of curvature obtain open set orthogonal parallel transport parametrized by arc parametrized curve parametrized surface plane curve point p e proof Prop PROPOSITION prove regular curve regular surface Remark restriction ruled surface segment Show sphere S2 straight line subset surface of revolution tangent plane tangent vector Tp(S unit vector variation vector field zero