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hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean geometry.The parallel postulate of Euclidean geometry is replaced with: . For any given line R and point P not on R, in the plane containing both line R and point P there are at least two distinct lines through P that do not intersect R. math.ST is an alias for stat.TH. Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data ... download Foundations of hyperbolic manifolds pdf download
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hyperbolic space is a homogeneous space that has a constant negative curvature, where in this case the curvature is the sectional curvature.It is
hyperbolic geometry in more than 2 dimensions, and is distinguished from Euclidean spaces with zero curvature that define the Euclidean geometry, and elliptic geometry that have a constant positive curvature. e-books in
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Minkowski space can be considered to have a Euclidean metric with imaginary time coordinate where is the speed of light (by convention is normally used) and where i is the imaginary number.
Minkowski space unifies Euclidean three-space plus time (the "fourth dimension") in Einstein's theory of special relativity.
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Riemann sphere, also called the extended complex plane, is a one-dimensional complex manifold C^* (C-star) which is the one-point compactification of the complex numbers C^*=C union {infty^~}, together with two charts. (Here infty^~ denotes complex infinity.) The notation C^^ is also used (Krantz 1999, p. 82; Lorentzen, and Waadeland 2008, p. 3).
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