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open hypersurface

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  • Spacetime — For other uses of this term, see Spacetime (disambiguation). Two dimensional analogy of spacetime distortion. Matter changes the geometry of spacetime, this (curved) geometry being interpreted as gravity. White lines do not represent the… …   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

  • Affine focal set — In mathematics, and especially affine differential geometry, the affine focal set of a smooth submanifold M embedded in a smooth manifold N is the caustic generated by the affine normal lines. It can be realised as the bifurcation set of a… …   Wikipedia

  • Metric tensor — In the mathematical field of differential geometry, a metric tensor is a type of function defined on a manifold (such as a surface in space) which takes as input a pair of tangent vectors v and w and produces a real number (scalar) g(v,w) in a… …   Wikipedia

  • Bounded variation — In mathematical analysis, a function of bounded variation refers to a real valued function whose total variation is bounded (finite): the graph of a function having this property is well behaved in a precise sense. For a continuous function of a… …   Wikipedia

  • Microcanonical ensemble — Statistical mechanics Thermodynamics · …   Wikipedia

  • Plane (geometry) — Two intersecting planes in three dimensional space In mathematics, a plane is a flat, two dimensional surface. A plane is the two dimensional analogue of a point (zero dimensions), a line (one dimension) and a space (three dimensions). Planes can …   Wikipedia

  • Cosmic censorship hypothesis — The weak and the strong cosmic censorship hypotheses are two mathematical conjectures about the structure of singularities arising in general relativity. Singularities that arise in the solutions of Einstein s equations are typically hidden… …   Wikipedia

  • Tesseract — For other uses, see Tesseract (disambiguation). Tesseract 8 cell 4 cube Schlegel diagram Type Convex regular 4 polytope …   Wikipedia

  • Alcubierre drive — The Alcubierre metric, also known as the Alcubierre drive or Warp Drive, is a speculative mathematical model of a spacetime exhibiting features reminiscent of the fictional warp drive from Star Trek , which can travel Faster than light (although… …   Wikipedia

  • Partial differential equation — A visualisation of a solution to the heat equation on a two dimensional plane In mathematics, partial differential equations (PDE) are a type of differential equation, i.e., a relation involving an unknown function (or functions) of several… …   Wikipedia

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