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Levi-Civita connection
In
Riemannian geometry
, the
Levi-Civita connection
is a specific
connection
on the tangent bundle of a
manifold
. More specifically, it is the
torsion
-free
metric connection
, i.e., the torsion-free
connection
on the
tangent bundle
(an
affine connection
) preserving a given (
pseudo-
)
Riemannian metric
.
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