negative Gauss curvature

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• Curvature — In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this …   Wikipedia

• Gauss–Bonnet theorem — The Gauss–Bonnet theorem or Gauss–Bonnet formula in differential geometry is an important statement about surfaces which connects their geometry (in the sense of curvature) to their topology (in the sense of the Euler characteristic). It is named …   Wikipedia

• Gaussian curvature — In differential geometry, the Gaussian curvature or Gauss curvature of a point on a surface is the product of the principal curvatures, κ 1 and κ 2, of the given point. It is an intrinsic measure of curvature, i.e., its value depends only on how… …   Wikipedia

• Sectional curvature — In Riemannian geometry, the sectional curvature is one of the ways to describe the curvature of Riemannian manifolds. The sectional curvature K(σp) depends on a two dimensional plane σp in the tangent space at p. It is the Gaussian curvature of… …   Wikipedia

• Courbure De Gauss — La courbure de Gauss d une surface paramétrée X en X(P) est le produit des courbures principales. De manière équivalente, la courbure de Gauss est le déterminant de l endomorphisme de Weingarten. Le tableau suivant liste les courbures de Gauss de …   Wikipédia en Français

• Courbure de gauss — La courbure de Gauss d une surface paramétrée X en X(P) est le produit des courbures principales. De manière équivalente, la courbure de Gauss est le déterminant de l endomorphisme de Weingarten. Le tableau suivant liste les courbures de Gauss de …   Wikipédia en Français

• Courbure de Gauss — La courbure de Gauss d une surface paramétrée X en X(P) est le produit des courbures principales. De manière équivalente, la courbure de Gauss est le déterminant de l endomorphisme de Weingarten. Le tableau suivant liste les courbures de Gauss de …   Wikipédia en Français

• Scalar curvature — In Riemannian geometry, the scalar curvature (or Ricci scalar) is the simplest curvature invariant of a Riemannian manifold. To each point on a Riemannian manifold, it assigns a single real number determined by the intrinsic geometry of the… …   Wikipedia

• Principal curvature — Saddle surface with normal planes in directions of principal curvatures In differential geometry, the two principal curvatures at a given point of a surface are the eigenvalues of the shape operator at the point. They measure how the surface… …   Wikipedia

• Differential geometry of surfaces — Carl Friedrich Gauss in 1828 In mathematics, the differential geometry of surfaces deals with smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives:… …   Wikipedia

• Riemannian geometry — Elliptic geometry is also sometimes called Riemannian geometry. Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a Riemannian metric , i.e. with an inner product on the tangent… …   Wikipedia