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Additional
Riemannian manifold
English Wikipedia - The Free Encyclopedia
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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
on the
tangent space
at each point
that varies smoothly from point to point in the sense that if
X
and
Y
are
vector fields
on
M
, then is a
smooth function
. The family of inner products is called a
Riemannian metric (tensor)
. These terms are named after the German mathematician
Bernhard Riemann
. The study of Riemannian manifolds constitutes the subject called
Riemannian geometry
.
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