## Differential Geometry: A First CourseDifferential Geometry: A First Course is an introduction to the classical theory of space curves and surfaces offered at the under Graduate and Post-Graduate courses in Mathematics. Based on Serret-Frenet formulae, the theory of space curves is developed and concluded with a detailed discussion on fundamental existence theorem. |

### What people are saying - Write a review

User Review - Flag as inappropriate

ddd

### Contents

Theory of Space Curves | 1 |

The First Fundamental Form and Local Intrinsic | 101 |

Geodesies on a Surface | 160 |

The Second Fundamental Form and Local | 279 |

The Fundamental Equations of Surface Theory | 382 |

Hints and Answers to Exercises | 444 |

455 | |

### Common terms and phrases

2Mdudv arc length asymptotic lines axis base curve binormal characteristic line Christoffel symbols circle condition cone corresponding cos2 curves are orthogonal cylinder Definition developable surface differential equation direction coefficients ds ds ds Dupin indicatrix edge of regression Example formula function fundamental coefficients fundamental form Gaussian curvature geodesic curvature geodesic equations given curve gives Hence Integrating intersection involute isometric Ldu2 let us find line of striction lines of curvature locus mapping metric Ndv2 normal curvature Note obtain orthogonal trajectories osculating plane osculating sphere parallel parametric curves parametric representation perpendicular plane curve position vector principal curvatures principal directions principal normal properties prove radius right helicoid ruled surface similar manner sin2 space curve spherical curvature straight line Substituting surface normal surface of revolution Taking dot product tangent plane unit vector values XOZ plane z-axis zero