differentiable manifold

In particular it is possible to use calculus on a differentiable manifold.

The general setting for the study of differential forms is on a differentiable manifold.

It is possible to develop a calculus for differentiable manifolds.

It is generally concerned with geometric structures on differentiable manifolds.

This is the standard way differentiable manifolds are defined.

Similarly for a differentiable manifold it has to be a diffeomorphism.

Similarly, if X is a differentiable manifold, then the group elements are diffeomorphisms.

Each point of an n-dimensional differentiable manifold has a tangent space.

The study of calculus on differentiable manifolds is known as differential geometry.

A volume form provides a means to define the integral of a function on a differentiable manifold.

Smooth vector field on a differentiable manifold, see the tangent space.

Any differentiable manifold can be given a Riemannian structure.

The Ricci flow was only defined for smooth differentiable manifolds.

Derivatives are defined as is usual for a differentiable manifold:

It also defines a measure, but exists on any differentiable manifold, orientable or not.

This relies the dimension of a variety to that of a differentiable manifold.

The functions below are generally used to build up partitions of unity on differentiable manifolds.

There are a number of important motivations for studying differentiable manifolds within this abstract framework.

It is the study of a geometric structure called a contact structure on a differentiable manifold.

Each fiber is a non-compact differentiable manifold of real dimension .

Thus dimension 4 differentiable manifolds are the most complicated:

Hermann Weyl gave an intrinsic definition for differentiable manifolds in 1912.

The tangent space is the generalization to higher-dimensional differentiable manifolds.

More generally, it is an element of the canonical bundle of a differentiable manifold.

Differentiable manifolds are very important in physics.