A Comprehensive Introduction to Differential Geometry, Volume 4Publish or Perish, Incorporated, 1975 - Geometry, Differential |
Contents
Higher Dimensions and Codimensions | 1 |
The Fundamental Equations for Submanifolds | 46 |
Elements of the Theory of Surfaces in R Chapter 3 A Compendium of Surfaces Chapter 4 Curves on Surfaces Chapter 5 Complete Surfaces of Consta... | 134 |
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Common terms and phrases
arclength choose Codazzi-Mainardi equations compact conformal map conjugate points connected consider constant curvature convex coordinate system Corollary covariant curve cut point define denote diffeomorphism dxdy everywhere formula Gauss geodesic mapping hypersurfaces imbedding implies inner product intersection isometry Jacobi field k-forms K₁ k₂ Lemma length linear M₂ manifold of constant mean curvature metric minimal geodesic minimal surface minimum n-dimensional neighborhood non-zero normal bundle obtain oriented orthogonal parameterized plane principal curvatures Proof Proposition prove result Riemannian manifold satisfies second fundamental form sectional curvatures shows sphere submanifold subspace Suppose tangent vectors tensor Theorem totally geodesic umbilics unit normal V₁ variation vector field vector field W₂ X₁ Y₁ Y₂ zero θα ΡεΜ ду Эх