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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In differentialgeometry, an affine connection is a geometric object on a smooth manifold which connects nearby tangent spaces, so it permits tangent vector...
In Euclidean geometry, an affine transformation or affinity (from the Latin, affinis, "connected with") is a geometric transformation that preserves lines...
Differentialgeometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It...
In mathematics, affinegeometry is what remains of Euclidean geometry when ignoring (mathematicians often say "forgetting") the metric notions of distance...
Information geometry is an interdisciplinary field that applies the techniques of differentialgeometry to study probability theory and statistics. It...
parallel line segments. Affine space is the setting for affinegeometry. As in Euclidean space, the fundamental objects in an affine space are called points...
See tensor. Affinedifferentialgeometry, a geometry that studies differential invariants under the action of the special affine group Affine gap penalty...
coherent sheaves on affine complex varieties. Complex geometry also makes use of techniques arising out of differentialgeometry and analysis. For example...
are disregarded—projective geometry that consider only alignment of points but not distance and parallelism, affinegeometry that omits the concept of...
elliptic, spherical or affinegeometry. Axioms of continuity and "betweenness" are also optional, for example, discrete geometries may be created by discarding...
of differential and analytic manifolds. This is obtained by extending the notion of point: In classical algebraic geometry, a point of an affine variety...
In differentialgeometry, an affine manifold is a differentiable manifold equipped with a flat, torsion-free connection. Equivalently, it is a manifold...
(the affine transformations). The first issue for geometers is what kind of geometry is adequate for a novel situation. Unlike in Euclidean geometry, the...
1931 for dissertation entitled The relation between affine and projective differentialgeometry. During his time in Tohoku Imperial University, Su met...
when a metric can be found so that a given differential form is harmonic, and various works on affinegeometry. In the comments on his collected works in...
classical differentialgeometryPages displaying short descriptions of redirect targets Differentiable curve – Study of curves from a differential point of...
In mathematics, the differentialgeometry of surfaces deals with the differentialgeometry of smooth surfaces with various additional structures, most...
especially differentialgeometry, an affine sphere is a hypersurface for which the affine normals all intersect in a single point. The term affine sphere...
In mathematics, projective differentialgeometry is the study of differentialgeometry, from the point of view of properties of mathematical objects such...
"Affinedifferentialgeometry", Encyclopedia of Mathematics, EMS Press Spivak, Michael (1999), A Comprehensive introduction to differentialgeometry (Volume...
In the mathematical field of differentialgeometry, the affinegeometry of curves is the study of curves in an affine space, and specifically the properties...
parallelism. Affinegeometry of curves The study of curve properties that are invariant under affine transformations. Affinedifferentialgeometry A type of...
affinedifferentialgeometry, the affine focal set of a smooth submanifold M embedded in a smooth manifold N is the caustic generated by the affine normal...
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