Differential Geometry of Curves and Surfaces, Seite 2Prentice-Hall, 1976 - 503 Seiten This volume covers local as well as global differential geometry of curves and surfaces. |
Inhalt
Regular Surfaces | 51 |
The Geometry of the Gauss Map | 134 |
The Intrinsic Geometry of Surfaces | 217 |
Urheberrecht | |
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angle appendix to Chap arc length arcwise connected Assume asymptotic curves axis closed curve coefficients compact complete surface const constant contained convex coordinate curves coordinate neighborhood cylinder defined definition denote diffeomorphism differentiable function differentiable map differential geometry e₁ equations Example Exercise fact Figure follows fundamental form Gauss Gauss-Bonnet theorem Gaussian curvature geodesic given hence homeomorphism intersection isometry Jacobi field k₁ k₂ 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 unit vector V₁ V₂ vector field w₁ w₂ zero ди