In differential geometry, a one-form (or covector field) on a differentiable manifold is a differential form of degree one, that is, a smooth section...

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

manifolds. The modern notion of differential forms was pioneered by Élie Cartan. It has many applications, especially in geometry, topology and physics. For...

Riemannian differential geometry is that affine differential geometry studies manifolds equipped with a volume form rather than a metric. Here we consider the...

Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds...

sophisticated ones. Roughly speaking, the pullback mechanism (using precomposition) turns several constructions in differential geometry into contravariant...

In differential geometry, a Lie-algebra-valued form is a differential form with values in a Lie algebra. Such forms have important applications in the...

differential topology is distinct from the closely related field of differential geometry, which concerns the geometric properties of smooth manifolds, including...

In differential geometry, the curvature form describes curvature of a connection on a principal bundle. The Riemann curvature tensor in Riemannian geometry...

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

mathematics such as calculus, differential geometry, algebraic geometry and algebraic topology. The term differential is used nonrigorously in calculus...

the kernel of a differential one-form, and the non-integrability condition translates into a maximal non-degeneracy condition on the form. These conditions...

In differential geometry, a discipline within mathematics, a distribution on a manifold M {\displaystyle M} is an assignment x ↦ Δ x ⊆ T x M {\displaystyle...

In differential geometry, the second fundamental form (or shape tensor) is a quadratic form on the tangent plane of a smooth surface in the three-dimensional...

geometry in large part because they allow a comparison between the local geometry at one point and the local geometry at another point. Differential geometry...

applications in differential geometry. On complex manifolds, they are fundamental and serve as the basis for much of algebraic geometry, Kähler geometry, and Hodge...

Foundations of Differential Geometry is an influential 2-volume mathematics book on differential geometry written by Shoshichi Kobayashi and Katsumi Nomizu...

analysis. Complex geometry sits at the intersection of algebraic geometry, differential geometry, and complex analysis, and uses tools from all three areas...

and differential topology, a closed form is a differential form α whose exterior derivative is zero (dα = 0); and an exact form is a differential form, α...

refer to two different formulae in differential geometry or algebraic topology. The Cartan formula in differential geometry states: L X = d ι X + ι X d {\displaystyle...

qualunque". Mem. Acc. Lincei. 2 (5): 276–322. Sharpe, R. W. (1997). Differential Geometry: Cartan's Generalization of Klein's Erlangen Program. New York:...

In differential geometry a translation surface is a surface that is generated by translations: For two space curves c 1 , c 2 {\displaystyle c_{1},c_{2}}...

{\displaystyle T^{*}Q} that preserve this definition, up to a total differential (exact form), may be called canonical coordinates; transformations between...

methods—differential geometry, algebraic geometry, computational geometry, algebraic topology, discrete geometry (also known as combinatorial geometry), etc...

Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and the Euclidean space by methods of differential...

In differential geometry, an equivariant differential form on a manifold M acted upon by a Lie group G is a polynomial map α : g → Ω ∗ ( M ) {\displaystyle...

(orthogonal groups), differential geometry (the Riemannian metric, the second fundamental form), differential topology (intersection forms of manifolds, especially...

specifically differential geometry, a connection form is a manner of organizing the data of a connection using the language of moving frames and differential forms...

vector-valued differential form on a manifold M is a differential form on M with values in a vector space V. More generally, it is a differential form with values...

In mathematics, in particular in differential geometry, mathematical physics, and representation theory, a Weitzenböck identity, named after Roland Weitzenböck...