Dodatkowe przykłady dopasowywane są do haseł w zautomatyzowany sposób - nie gwarantujemy ich poprawności.
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.