Translate:
English
Chinese (S)
Chinese (T)
Croatian
Dutch
French
German
Hebrew
Italian
Japanese
Korean
Portuguese
Russian
Serbian
Spanish
Swedish
Turkish
Additional
Riemannian connection on a surface
English Wikipedia - The Free Encyclopedia
Download this dictionary
Riemannian connection on a surface
For the classical approach to the geometry of surfaces, see
Differential geometry of surfaces
.
In
mathematics
, the
Riemannian connection on a
surface
or
Riemannian 2-manifold
refers to several intrinsic geometric structures discovered by
Tullio Levi-Civita
,
Élie Cartan
and
Hermann Weyl
in the early part of the twentieth century:
parallel transport
,
covariant derivative
and
connection form
. These concepts were put in their final form using the language of
principal bundles
only in the 1950s. The classical nineteenth century approach to the
differential geometry of surfaces
, due in large part to
Carl Friedrich Gauss
, has been reworked in this modern framework, which provides the natural setting for the classical theory of the
moving frame
as well as the
Riemannian geometry
of higher-dimensional
Riemannian manifolds
. This account is intended as an introduction to the theory of
connections
.
See more at Wikipedia.org...
© This article uses material from
Wikipedia
®
and is licensed under the
GNU Free Documentation License
and under the
Creative Commons Attribution-ShareAlike License