positive 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

• Gauss–Codazzi equations — In Riemannian geometry, the Gauss–Codazzi–Mainardi equations are fundamental equations in the theory of embedded hypersurfaces in a Euclidean space, and more generally submanifolds of Riemannian manifolds. They also have applications for embedded …   Wikipedia

• Curvature of Riemannian manifolds — In mathematics, specifically differential geometry, the infinitesimal geometry of Riemannian manifolds with dimension at least 3 is too complicated to be described by a single number at a given point. Riemann introduced an abstract and rigorous… …   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

• Mean curvature — In mathematics, the mean curvature H of a surface S is an extrinsic measure of curvature that comes from differential geometry and that locally describes the curvature of an embedded surface in some ambient space such as Euclidean space. The… …   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

• Generalized Gauss–Bonnet theorem — In mathematics, the generalized Gauss–Bonnet theorem (also called Chern–Gauss–Bonnet theorem) presents the Euler characteristic of a closed even dimensional Riemannian manifold as an integral of a certain polynomial derived from its curvature. It …   Wikipedia

• Carl Friedrich Gauss — Infobox Scientist box width = 300px name = Carl Friedrich Gauss caption = Johann Carl Friedrich Gauss (1777 1855), painted by Christian Albrecht Jensen birth date = birth date|1777|4|30|df=y birth place = Braunschweig, Electorate of Brunswick… …   Wikipedia