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searching for cotangent space 17 found (49 total)

Quadratic differential (394 words) [view diff] exact match in snippet view article find links to article

differentials on a Riemann surface has a natural interpretation as the cotangent space to the Riemann moduli space, or Teichmüller space. Each quadratic differential

Analytic space (1,031 words) [view diff] exact match in snippet view article find links to article

vanishing at x, then the cotangent space at x is mx / mx2. The tangent space is (mx / mx2)*, the dual vector space to the cotangent space. Analytic mappings

Fano surface (742 words) [view diff] exact match in snippet view article find links to article

powerful applications. By example, one can recover the fact that the cotangent space of S is generated by global sections. This space of global 1-forms

Weil–Petersson metric (439 words) [view diff] exact match in snippet view article find links to article

Teichmüller space is represented by a Riemann surface R, then the cotangent space at that point can be identified with the space of quadratic differentials

Atiyah–Singer index theorem (7,529 words) [view diff] exact match in snippet view article find links to article

function on the cotangent bundle of X, homogeneous of degree n on each cotangent space. (In general, differential operators transform in a rather complicated

Integrability conditions for differential systems (1,055 words) [view diff] exact match in snippet view article find links to article

orthogonal coframe θi, i.e., a collection of 1-forms forming a basis of the cotangent space at every point with ⟨ θ i , θ j ⟩ = δ i j {\displaystyle \langle \theta

Schouten–Nijenhuis bracket (1,153 words) [view diff] exact match in snippet view article find links to article

symmetric multivector fields can be identified with functions on the cotangent space T ∗ M {\displaystyle T^{*}M} of M {\displaystyle M} that are polynomial

Phase space (2,123 words) [view diff] exact match in snippet view article find links to article

local Darboux coordinates for the standard symplectic structure on a cotangent space. The motion of an ensemble of systems in this space is studied by classical

W. V. D. Hodge (1,360 words) [view diff] exact match in snippet view article find links to article

number p of holomorphic differentials dzi wedged to make up α (the cotangent space being spanned by the dzi and their complex conjugates). The dimensions

Witten conjecture (1,167 words) [view diff] exact match in snippet view article find links to article

on Mg,n, whose fiber at a point of the moduli stack is given by the cotangent space of a Riemann surface at the marked point xi. The intersection index

Irregularity of a surface (929 words) [view diff] exact match in snippet view article find links to article

F to its Albanese variety A which induces a homomorphism from the cotangent space of the Albanese variety (of dimension q) to H1,0(F). Jun-Ichi Igusa

Differential operator (3,693 words) [view diff] exact match in snippet view article find links to article

|=k}\sum _{\mu }P_{\nu \mu }^{\alpha }(x)\xi _{\alpha }u_{\mu }.} In the cotangent space over a fixed point x of X, the symbol σ P {\displaystyle \sigma _{P}}

Gradient (5,702 words) [view diff] exact match in snippet view article find links to article

space R n {\displaystyle \mathbb {R} ^{n}} itself, and similarly the cotangent space at each point can be naturally identified with the dual vector space

Teichmüller space (4,994 words) [view diff] exact match in snippet view article find links to article

differentials on a Riemann surface X {\displaystyle X} are identified with the cotangent space at ( X , f ) {\displaystyle (X,f)} to Teichmüller space. The Weil–Petersson

First-class constraint (4,556 words) [view diff] exact match in snippet view article find links to article

its position x in the base manifold S and its position within the cotangent space p, then we have a constraint f = m2 −g(x)−1(p,p) = 0. The Hamiltonian

Kähler identities (4,200 words) [view diff] exact match in snippet view article find links to article

\beta \rangle } is the inner product on the exterior products of the cotangent space of X {\displaystyle X} induced by the Riemannian metric. Using this

Optical metric (4,262 words) [view diff] exact match in snippet view article find links to article

{\displaystyle {\boldsymbol {\alpha }}} is an automorphism of a subspace of the cotangent space defined by orthogonality with respect to the observer. In other words