## Differentiable manifold |

In mathematics, a **differentiable manifold** is a type of

In formal terms, a **differentiable manifold** is a
*locally* by using the
*transition maps.*

Differentiability means different things in different contexts including:
*k* times differentiable,

- history
- definition
- alternative definitions
- differentiable functions
- bundles
- calculus on manifolds
- topology of differentiable manifolds
- structures on manifolds
- generalizations
- see also
- notes
- references
- bibliography

The emergence of differential geometry as a distinct discipline is generally credited to
^{
[1]} before the faculty at Göttingen. He motivated the idea of a manifold by an intuitive process of varying a given object in a new direction, and presciently described the role of coordinate systems and charts in subsequent formal developments:

*Having constructed the notion of a manifoldness of n dimensions, and found that its true character consists in the property that the determination of position in it may be reduced to n determinations of magnitude, ...*– B. Riemann

The works of physicists such as
^{
[2]} and mathematicians
^{
[3]} led to the development of
^{
[4]} The widely accepted general definition of a manifold in terms of an
^{
[5]}

Other Languages

català: Varietat diferenciable

Deutsch: Differenzierbare Mannigfaltigkeit

español: Variedad diferenciable

français: Variété différentielle

한국어: 매끄러운 다양체

italiano: Varietà differenziabile

Nederlands: Differentieerbare variëteit

日本語: 可微分多様体

polski: Rozmaitość różniczkowa

русский: Гладкое многообразие

Tagalog: Manipoldong diperensiyable

Türkçe: Diferansiyellenebilir manifold

українська: Диференційовний многовид

中文: 微分流形