Tensor Calculus Through Differential Geometry |
Contents
The Twodimensional Curved Surface | 13 |
Special Results | 23 |
Some Riemannian Geometry | 39 |
Copyright | |
5 other sections not shown
Common terms and phrases
a₁₁ aaß angle arbitrary arc length ax¹ basis vectors body forces Cartesian catenoid Christoffel symbols const constant contravariant coordinate curves coordinate system covariant differentiation covariant vector curvilinear coordinates da¹ da² defined derivative dh₁ di₂ dimensions directions ds² du¹du² du² duß dx¹ enveloping space equation expression əxi Figure fluid function fundamental tensor g₁ Gauss-Bonnet theorem Gaussian curvature geometry given point giving grad h₁ du¹ h₂ i₁ i₂ integral lines of curvature mean curvature metric motion n₁ normal notation orthogonal parameter particle physical components plane R₁ Riemannian right conoid ruled surface scalar Section sin² surface normal surface vector symmetric theorem transformation law two-dimensional unit vector velocity viscous z₁ zero δε δι ат даа дда ди ди² диа дих див дх