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Lie derivative of an affine connection
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Physics
Branch of physics
General relativity
Covariant derivative
Levi-Civita connection
Created
2026-09-24
Updated
2026-09-24
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The
Lie derivative
of
a
connection is the
tensor
(
L
X
∇
)
Y
Z
=
L
X
(
∇
Y
Z
)
−
∇
L
X
Y
Z
−
∇
Y
(
L
X
Z
)
.
(1)
An
isometry
preserves the
Levi-Civita connection
, so
L
K
∇
=
0
for
a
Killing vector field
.
Ancestors
(6)
Levi-Civita connection
Covariant derivative
General relativity
Branch of physics
Physics
Home
Incoming links
(1)
Past exam of the mathematics course of the University of Cambridge
/
2026
/
iii
/
Paper 309
/
1
/
b
/
Solution
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