Faster access than browser!Similarities between Differential geometry and Lie derivative
Differential geometry and Lie derivative have 16 things in common (in Unionpedia): Affine connection, Connection (mathematics), Covariant derivative, Diffeomorphism, Differentiable manifold, Differential form, Directional derivative, Exterior derivative, Group (mathematics), Levi-Civita connection, Lie group, Riemannian manifold, Smoothness, Tangent bundle, Tensor, Vector field.
Affine connection
In the branch of mathematics called differential geometry, an affine connection is a geometric object on a smooth manifold which connects nearby tangent spaces, so it permits tangent vector fields to be differentiated as if they were functions on the manifold with values in a fixed vector space.
Affine connection and Differential geometry · Affine connection and Lie derivative ·
Connection (mathematics)
In geometry, the notion of a connection makes precise the idea of transporting data along a curve or family of curves in a parallel and consistent manner.
Connection (mathematics) and Differential geometry · Connection (mathematics) and Lie derivative ·
Covariant derivative
In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold.
Covariant derivative and Differential geometry · Covariant derivative and Lie derivative ·
Diffeomorphism
In mathematics, a diffeomorphism is an isomorphism of smooth manifolds.
Diffeomorphism and Differential geometry · Diffeomorphism and Lie derivative ·
Differentiable manifold
In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a linear space to allow one to do calculus.
Differentiable manifold and Differential geometry · Differentiable manifold and Lie derivative ·
Differential form
In the mathematical fields of differential geometry and tensor calculus, differential forms are an approach to multivariable calculus that is independent of coordinates.
Differential form and Differential geometry · Differential form and Lie derivative ·
Directional derivative
In mathematics, the directional derivative of a multivariate differentiable function along a given vector v at a given point x intuitively represents the instantaneous rate of change of the function, moving through x with a velocity specified by v. It therefore generalizes the notion of a partial derivative, in which the rate of change is taken along one of the curvilinear coordinate curves, all other coordinates being constant.
Differential geometry and Directional derivative · Directional derivative and Lie derivative ·
Exterior derivative
On a differentiable manifold, the exterior derivative extends the concept of the differential of a function to differential forms of higher degree.
Differential geometry and Exterior derivative · Exterior derivative and Lie derivative ·
Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.
Differential geometry and Group (mathematics) · Group (mathematics) and Lie derivative ·
Levi-Civita connection
In Riemannian geometry, the Levi-Civita connection is a specific connection on the tangent bundle of a manifold.
Differential geometry and Levi-Civita connection · Levi-Civita connection and Lie derivative ·
Lie group
In mathematics, a Lie group (pronounced "Lee") is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure.
Differential geometry and Lie group · Lie derivative and Lie group ·
Riemannian manifold
In differential geometry, a (smooth) Riemannian manifold or (smooth) Riemannian space (M,g) is a real, smooth manifold M equipped with an inner product g_p on the tangent space T_pM at each point p that varies smoothly from point to point in the sense that if X and Y are differentiable vector fields on M, then p \mapsto g_p(X(p),Y(p)) is a smooth function.
Differential geometry and Riemannian manifold · Lie derivative and Riemannian manifold ·
Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.
Differential geometry and Smoothness · Lie derivative and Smoothness ·
Tangent bundle
In differential geometry, the tangent bundle of a differentiable manifold M is a manifold TM which assembles all the tangent vectors in M. As a set, it is given by the disjoint unionThe disjoint union ensures that for any two points x1 and x2 of manifold M the tangent spaces T1 and T2 have no common vector.
Differential geometry and Tangent bundle · Lie derivative and Tangent bundle ·
Tensor
In mathematics, tensors are geometric objects that describe linear relations between geometric vectors, scalars, and other tensors.
Differential geometry and Tensor · Lie derivative and Tensor ·
Vector field
In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space.
Differential geometry and Vector field · Lie derivative and Vector field ·
The list above answers the following questions
- What Differential geometry and Lie derivative have in common
- What are the similarities between Differential geometry and Lie derivative
Differential geometry and Lie derivative Comparison
Differential geometry has 141 relations, while Lie derivative has 72. As they have in common 16, the Jaccard index is 7.51% = 16 / (141 + 72).
References
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