## Tensor Calculus Through Differential Geometry |

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### Contents

The Twodimensional Curved Surface | 13 |

Special Results | 23 |

Some Riemannian Geometry | 39 |

Copyright | |

5 other sections not shown

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### Common terms and phrases

angle arbitrary arc length assuming asymptotic lines basis vectors body forces Cartesian catenoid Christoffel brackets Christoffel symbols consider const constant contravariant components coordinate curves coordinate system covariant components covariant differentiation covariant vector curved surface curvilinear coordinates defined denoted differential geometry differentiation with respect enveloping space expression extreme values Figure fluid function of position fundamental tensor Gauss Gauss-Bonnet theorem Gaussian curvature geodesic coordinates given point giving grad indices integral isometric line of striction linear lines of curvature matrix mean curvature metric ds2 momentum non-vanishing parallel parameter particle perpendicular physical components polar principal directions right conoid ruled surface scalar Section sin2 space vector surface normal surface of revolution surface vector symmetric tangent vector tensor calculus tensor form theorem transformation law unit vector vector field vector product velocity viscous zero