Differential Geometry of Curves and Surfaces, Sida 2Prentice-Hall, 1976 - 503 sidor This volume covers local as well as global differential geometry of curves and surfaces. |
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87 sidor matchar do carmo i den här boken
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Sida 498
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Innehåll
Regular Surfaces | 51 |
The Geometry of the Gauss Map | 134 |
The Intrinsic Geometry of Surfaces | 217 |
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Differential Geometry of Curves and Surfaces, Sida 2 Manfredo Perdigão do Carmo Fragmentarisk förhandsgranskning - 1976 |
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angle appendix to Chap arc length arcwise connected Assume asymptotic curves axis closed curve coefficients compact complete surface conjugate const constant contained convex coordinate curves coordinate neighborhood cylinder defined definition denote diffeomorphism differentiable function differentiable map e₁ e₂ equations Example Exercise fact Figure follows fundamental form Gauss Gauss map 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 sphere surface of revolution t₁ tangent plane tangent vector theorem unit vector V₁ V₂ vector field w₁ w₂ zero ди дх