Euclidean geometry in nLab
In euclidean n n -space for n > 2 n\gt 2 a general conformal transformation is some composition of a translation, dilation, rotation and ...
On Euclidean geometry: Saunders Mac Lane, Metric postulates for plane geometry, American Mathematical Monthly, 66 7 (1959) 543-555. (doi ...
Let V ∈ RO ( G ) V \in RO(G) be an orthogonal linear representation of a finite group G G on a real vector space V V . If G G is the point group ...
which constitutes an exceptional calibration of ℝ 4 \mathbb{R}^4 with its Euclidean geometry. More generally, a Spin(7)-manifold carries a ...
geometry of physics – supergeometry. Superalgebra. super commutative ... super Euclidean group · super ∞-groupoid · super formal smooth ...
On (isometric) submanifolds of Euclidean space via (the algebraic geometry of) their higher-dimensional coframe fields: Phillip Griffiths, ...
geometry of physics -- supergeometry in nLab
Supergeometry is the generalization of differential geometry (or algebraic geometry) to the situation where algebras of functions are generalized.
1. Idea ; positive number sectional curvature are the topic of elliptic geometry; ; zero sectional curvature are the topic of Euclidean geometry;.
Isbell duality is the archetype of the duality between geometry and algebra that permeates mathematics (such as Gelfand duality, Stone duality, or the ...
The real line ℝ \mathbb{R} models the naive intuition of the geometric line in Euclidean geometry. See also at complex line. In many contexts of ...
noncommutative algebraic geometry in nLab
Commutative algebraic geometry, restricts attention to spaces whose local description is via commutative rings and algebras, while ...
Typically the term is used in generalization of curves and surfaces that are embedded into an ambient Cartesian space/Euclidean space – such as ...
Euclidean space · real line, plane · cylinder, cone · sphere, ball · circle ... geometry into algebraic geometry. For instance, the category of ...
torsion of a metric connection in nLab
In supergeometry a metric structure is given by a connection with values in the super Poincaré Lie algebra. The corresponding notion of torsion ...
Euclidean geometry · Riemannian geometry · affine connection · Euclidean gravity · Poincaré group Iso ( d − 1 , 1 ) Iso(d-1,1), Lorentz group O ...
Euclidean geometry, hyperbolic geometry, elliptic geometry. (pseudo ... Jürgen Jost, Riemannian Geometry and Geometric Analysis ...
Proposition 3.2. Every connected finite-dimensional real Lie group is homeomorphic to a product of a compact Lie group and a Euclidean space.
... Euclidean spaces ℝ n \mathbb{R}^n , an ... Orbifolds are in differential geometry what Deligne-Mumford stacks are in algebraic geometry.
In the geometry of symmetric spaces, one defines transvections using a parallel transport along geodesic lines; at any point these transvections ...
nLab differential forms in synthetic differential geometry
In the context of synthetic differential geometry a differential form ω \omega of degree k k on a manifold X X is literally a function on the ...