Space form information

mathematics, a space form is a complete Riemannian manifold M of constant sectional curvature K. The three most fundamental examples are Euclidean n-space, the...

In geometric topology, the spherical space form conjecture (now a theorem) states that a finite group acting on the 3-sphere is conjugate to a group of...

Unique Forms of Continuity in Space (Italian: Forme uniche della continuità nello spazio) is a 1913 bronze Futurist sculpture by Umberto Boccioni. It is...

quadratic form on a vector space. The study of quadratic forms, in particular the question of whether a given integer can be the value of a quadratic form over...

In mathematics, a bilinear form is a bilinear map V × V → K on a vector space V (the elements of which are called vectors) over a field K (the elements...

wider sense, the form is the way something happens. Form may also refer to: Form (document), a document (printed or electronic) with spaces in which to write...

of the elements of a real vector space form a real coordinate space of the same dimension as that of the vector space. Similarly, the Cartesian coordinates...

electric current distribution in space Form factor (electronics), characterizing the functional form of oscillating signals Form factor (radiative transfer)...

Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, in Euclid's Elements, it was the three-dimensional...

for definitions of other related terms. The meagre subsets of a fixed space form a σ-ideal of subsets; that is, any subset of a meagre set is meagre, and...

metric tensor, the Ricci tensor assigns to each tangent space of the manifold a symmetric bilinear form (Besse 1987, p. 43). Broadly, one could analogize the...

assuming the summation convention). When a vector space is equipped with a nondegenerate bilinear form (or metric tensor as it is often called in this context)...

vector space is a vector space V over a field F (for example the real numbers R) equipped with a symplectic bilinear form. A symplectic bilinear form is a...

form is a generalization of a bilinear form that, in turn, is a generalization of the concept of the dot product of Euclidean space. A bilinear form is...

mathematics, a linear form (also known as a linear functional, a one-form, or a covector) is a linear map from a vector space to its field of scalars...

Otherwise the it is a definite quadratic form. More explicitly, if q is a quadratic form on a vector space V over F, then a non-zero vector v in V is...

Riesz (Riesz 1910). Lp spaces form an important class of Banach spaces in functional analysis, and of topological vector spaces. Because of their key role...

n-dimensional sphere or hyperbolic space, or more generally a pseudo-Riemannian space form, and the hyperplanes are the hypersurfaces consisting of all geodesics...

Riemannian manifold is a space form if its sectional curvature is equal to a constant K. The Riemann tensor of a space form is given by R a b c d = K...

and ergodic theory (which forms the mathematical underpinning of thermodynamics). John von Neumann coined the term Hilbert space for the abstract concept...

neighborhoods. A T3 space or regular Hausdorff space is a topological space that is both regular and a Hausdorff space. (A Hausdorff space or T2 space is a topological...

In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, may be added together and multiplied...

In abstract algebra and multilinear algebra, a multilinear form on a vector space V {\displaystyle V} over a field K {\displaystyle K} is a map f : V k...