Laplacian operators in differential geometry

•  Differential geometry

  Differential geometry is a mathematical discipline that uses the methods of differential and integral calculus, as well as linear and multilinear algebra, to study problems in geometry. The theory of plane and space curves and of surfaces in the three-dimensional Euclidean space formed the basis for its initial development in the eighteenth and nineteenth century.

  

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•  Sphere

  A sphere (from Greek σφαῖρα—sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in three dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point. This distance r is known as the radius of the sphere. The maximum straight distance through the sphere is known as the diameter of the sphere.

  

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•  Symplectic manifold

  In mathematics, a symplectic manifold is a smooth manifold, M, equipped with a closed, nondegenerate, skew-symmetric 2-form, ω, called the symplectic form. The study of symplectic manifolds is called symplectic geometry or symplectic topology. Symplectic manifolds arise naturally in abstract formulations of classical mechanics and analytical mechanics as the cotangent bundles of manifolds, e.g.

  

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•  Tangent space

  In mathematics, the tangent space of a manifold is a concept which facilitates the generalization of vectors from affine spaces to general manifolds, since in the latter case one cannot simply subtract two points to obtain a vector pointing from one to the other.

  

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•  Tangent

  In geometry, the tangent line (or simply the tangent) to a curve at a given point is the straight line that "just touches" the curve at that point (in the sense explained more precisely below). As it passes through the point of tangency, the tangent line is "going in the same direction" as the curve, and in this sense it is the best straight-line approximation to the curve at that point. The same definition applies to space curves and curves in n-dimensional Euclidean space.

  

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•  Embedding

  In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup. When some object X is said to be embedded in another object Y, the embedding is given by some injective and structure-preserving map f : X → Y. The precise meaning of "structure-preserving" depends on the kind of mathematical structure of which X and Y are instances.

  

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•  Pseudosphere

  In geometry, a pseudosphere of radius R is any surface of curvature −1/R (precisely, a complete, simply connected surface of that curvature), by analogy with the sphere of radius R, which is a surface of curvature 1/R. The term was introduced by Eugenio Beltrami in his 1868 paper on models of hyperbolic geometry. The term is also used to refer to a certain surface called the tractricoid: the result of revolving a tractrix about its asymptote.

  

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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 is defined in different ways depending on the context.

  

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•  Shape of the Universe

  The shape of the Universe is an informal name for a subject of investigation within physical cosmology which describes the geometry of the universe including both local geometry and global geometry. It is loosely divided into curvature and topology, even though strictly speaking, it goes beyond both. More formally, the subject in practice investigates which 3-manifold corresponds to the spatial section in comoving coordinates of the 4-dimensional space-time of the Universe.

  

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•  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 after Carl Friedrich Gauss who was aware of a version of the theorem but never published it, and Pierre Ossian Bonnet who published a special case in 1848.

  

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• Differential geometry by likeorhate
• Differential operators by likeorhate

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•  Gavin Scott (screenwriter)

  Gavin Scott (born 1950) is a novelist, broadcaster and writer of the Emmy-winning mini-series The Mists of Avalon, DreamWorks’ Small Soldiers, Working Title’s The Borrowers and Sci Fi’s Legend of Earthsea, spent ten years making films for British television before becoming a screenwriter, creating more than two hundred documentaries and short films for BBC and the commercial TV, including UK’s prestigious Channel 4.

  

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•  Milk toast

  Milk toast is a breakfast food consisting of toasted bread and sugar dipped in or covered in hot milk into which a small amount of butter has been melted. Cinnamon and raisins may be added. Milk toast was a popular food throughout the late 19th century and early 20th century, especially for young children and for the ailing, for whom the food was thought to be soothing and easy to digest. Although not as popular today, milk toast is still considered a comfort food.

  

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•  Cold Lake Regional Airport

  Cold Lake Regional Airport,, is located 4 NM (7.4 km; 4.6 mi) west of Cold Lake, Alberta, Canada.

  

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•  Maduro (musician)

  Maduro is a Washington D.C. area electronic music artist who records dark, textured electronic music with world fusion influences. Maduro is signed with Octofoil Records. Maduro has appeared on compilations with Venetian Snares, Amon Tobin, Bassnectar, Beirut, Nouvelle Vague, and Muslimgauze.

  

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•  Yang Fang Leiden

  

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