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Convex Bodies and Convex Surfaces in
Manifolds of curvature not less than K The theorems
9 other sections not shown
Alexandrov analytic arbitrary point Ax and A2 Chapter closed convex surface coefficients congruent figures convex body convex cones convex hull coordinate vector corres curvature not less curves yi deformations of surfaces denote differentiable dihedral angles distance edge elliptic space equal equation of deformation Euclidean space E0 expressions external curvature figure F Fx and F2 Gaussian curvature geodesic curvature geodesic mapping Hence infinitesimal deformation infinitesimal displacement intersect isometric surfaces isometrically corresponding points join the points keeping in view lemma length line element line h locally convex manifold of curvature normal curvature obtain pair of isometric parameters plane of support point e0 points Ax polyhedron principal curvatures principal normal Proof rectilinear segments scalar product second quadratic form seen from inside semi-tangent shortest line space of curvature specific curvature straight line surface F tangent cone tangent vectors transformation unit vector velocity field vertex Weierstrass coordinates yi and y2