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...

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

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

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

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

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

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 smooth surface in three dimensions has a ridge point when a line of curvature has a local maximum or minimum of principal...

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...

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...

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...

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...

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

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

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...

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

conformal geometry is the study of the set of angle-preserving (conformal) transformations on a space. In a real two dimensional space, conformal geometry is...

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

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

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

Synthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is geometry without the use of coordinates. It relies on the axiomatic...

In differential geometry there are a number of second-order, linear, elliptic differential operators bearing the name Laplacian. This article provides...

invariant differential operators, and spherical functions, American Mathematical Society ISBN 0821826735 Sigurdur Helgason (2011) Integral Geometry and Radon...

structure, in terms of a system of differential forms. The idea is to take advantage of the way a differential form restricts to a submanifold, and the...

In differential geometry, the first fundamental form is the inner product on the tangent space of a surface in three-dimensional Euclidean space which...