## A Comprehensive Introduction to Differential Geometry, Volume 3Brandeis University, 1970 - Geometry, Differential |

### Contents

The Fundamental Equations for Hypersurfaces | 1 |

Covariant differentiation in a submanifold of a Riemannian manifold | 8 |

The moving frame description | 23 |

Copyright | |

22 other sections not shown

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### Common terms and phrases

1817 LIBRARIES angle asymptotic curve Chapter choose closed curve Codazzi-Mainardi equations compact oriented consider constant curvature convex coordinate system Corollary CR³ cylinder defined diffeomorphism direction elliptic formulas function Gauss Gauss-Bonnet Theorem Gaussian curvature geodesic homeomorphic immersion inner product integral curves intersect invariant inversion IR³ k₁ k₂ Lemma linearly independent lines of curvature matrix MICHIGAN Möbius strip moving frame neighborhood normal map obtain orthogonal orthonormal moving frame parabolic points parallel parameter curves parameterized by arclength perpendicular planar point positively oriented Problem Proof Proposition Riemannian manifold Riemannian metric ruled surface shows special affine sphere straight lines submanifold subset surface theory tangent developable tangent plane tangent vector tensor Theorem torus umbilics unit vector vector field X₁ z-axis zero ΡΕΜ