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Affine differential geometry information


Affine differential geometry is a type of differential geometry which studies invariants of volume-preserving affine transformations. The name affine differential geometry follows from Klein's Erlangen program. The basic difference between affine and Riemannian differential geometry is that affine differential geometry studies manifolds equipped with a volume form rather than a metric.

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Affine differential geometry

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Affine differential geometry is a type of differential geometry which studies invariants of volume-preserving affine transformations. The name affine...

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Affine

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See tensor. Affine differential geometry, a geometry that studies differential invariants under the action of the special affine group Affine gap penalty...

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Affine connection

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In differential geometry, an affine connection is a geometric object on a smooth manifold which connects nearby tangent spaces, so it permits tangent vector...

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Affine transformation

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In Euclidean geometry, an affine transformation or affinity (from the Latin, affinis, "connected with") is a geometric transformation that preserves lines...

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Differential geometry

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Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It...

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Information geometry

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Information geometry is an interdisciplinary field that applies the techniques of differential geometry to study probability theory and statistics. It...

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Affine geometry

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In mathematics, affine geometry is what remains of Euclidean geometry when ignoring (mathematicians often say "forgetting") the metric notions of distance...

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Affine space

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parallel line segments. Affine space is the setting for affine geometry. As in Euclidean space, the fundamental objects in an affine space are called points...

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Complex geometry

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coherent sheaves on affine complex varieties. Complex geometry also makes use of techniques arising out of differential geometry and analysis. For example...

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Outline of geometry

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Absolute geometry Affine geometry Algebraic geometry Analytic geometry Birational geometry Complex geometry Combinatorial geometry Computational geometry Conformal...

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Affine sphere

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especially differential geometry, an affine sphere is a hypersurface for which the affine normals all intersect in a single point. The term affine sphere...

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Projective differential geometry

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In mathematics, projective differential geometry is the study of differential geometry, from the point of view of properties of mathematical objects such...

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Geometry

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are disregarded—projective geometry that consider only alignment of points but not distance and parallelism, affine geometry that omits the concept of...

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List of geometers

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(1923–2023) Benoit Mandelbrot (1924–2010) – fractal geometry Katsumi Nomizu (1924–2008) – affine differential geometry Michael S. Longuet-Higgins (1925–2016) John...

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Eugenio Calabi

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when a metric can be found so that a given differential form is harmonic, and various works on affine geometry. In the comments on his collected works in...

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Algebraic geometry

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of differential and analytic manifolds. This is obtained by extending the notion of point: In classical algebraic geometry, a point of an affine variety...

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Synthetic geometry

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elliptic, spherical or affine geometry. Axioms of continuity and "betweenness" are also optional, for example, discrete geometries may be created by discarding...

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Affine manifold

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In differential geometry, an affine manifold is a differentiable manifold equipped with a flat, torsion-free connection. Equivalently, it is a manifold...

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Su Buqing

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1931 for dissertation entitled The relation between affine and projective differential geometry. During his time in Tohoku Imperial University, Su met...

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Geodesic

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classical differential geometryPages displaying short descriptions of redirect targets Differentiable curve – Study of curves from a differential point of...

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Projective geometry

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(the affine transformations). The first issue for geometers is what kind of geometry is adequate for a novel situation. Unlike in Euclidean geometry, the...

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Katsumi Nomizu

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subject was affine differential geometry, a topic to which he would return much later in his career. He presented his thesis, Invariant affine connections...

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Differential geometry of surfaces

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In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most...

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Affine curvature

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"Affine differential geometry", Encyclopedia of Mathematics, EMS Press Spivak, Michael (1999), A Comprehensive introduction to differential geometry (Volume...

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Affine geometry of curves

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In the mathematical field of differential geometry, the affine geometry of curves is the study of curves in an affine space, and specifically the properties...

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Riemannian geometry

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Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, defined as smooth manifolds with a Riemannian metric (an...

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Finite geometry

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inversive geometries. Finite geometries may be constructed via linear algebra, starting from vector spaces over a finite field; the affine and projective...

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