Differential Geometry of Curves and Surfaces, Page 2This volume covers local as well as global differential geometry of curves and surfaces. |
Contents
Regular Surfaces | 51 |
and Differentiability | 118 |
The Geometry of the Gauss Map | 134 |
Copyright | |
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Common terms and phrases
a₁ angle appendix to Chap arc length arcwise connected Assume asymptotic curves axis closed curve compact complete surface const constant contained convex coordinate curves coordinate neighborhood cylinder defined definition denote diffeomorphism differentiable function differentiable map e₁ equations Example Exercise fact Figure follows fundamental form Gauss Gauss map Gauss-Bonnet theorem Gaussian curvature geodesic geometry given hence homeomorphism intersection isometry Jacobi field k₁ Lemma local isometry minimal normal vector obtain open set orientation orthogonal p₁ parallel transport parametrized by arc parametrized curve parametrized surface plane curve proof Prop PROPOSITION prove regular curve regular parametrized regular surface ruled surface S₁ Show surface of revolution t₁ tangent plane tangent vector theorem U₁ unit vector V₁ vector field w₁ x₁ zero ди дх