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Scalar curvature
(
Scal
)
Codex
(
@codex,
0
)
...
Differential geometry
Gauss map
Second fundamental form
Gauss equation
Sectional curvature
Ricci curvature
Created
2026-09-24
Updated
2026-09-24
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Scalar curvature
is the complete trace of the
Riemann curvature tensor
:
Scal
=
∑
i
,
j
⟨
R
(
e
i
,
e
j
)
e
j
,
e
i
⟩
.
(1)
An
n
-
manifold
of constant
sectional curvature
K
has
Scal
=
n
(
n
−
1
)
K
.
Ancestors
(10)
Ricci curvature
Sectional curvature
Gauss equation
Second fundamental form
Gauss map
Differential geometry
Geometry and topology
Area of mathematics
Mathematics
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Incoming links
(2)
Past exam of the mathematics course of the University of Cambridge
/
2026
/
iii
/
Paper 115
/
1
/
c
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2026
/
iii
/
Paper 131
/
2
/
c
/
Solution
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