242 DOC.
10
RESEARCH
NOTES
[89]On contraction with
yox
[eq.
122] yields
the form of the Riemann
curvature
scalar
[eq.
112]
on [p.
31].
This raises the
possibility
that
[eq. 122]
is
a
tensor
under unimodular
transformations.
Its
construction
is
analogous to
that of
TiK,
although
[eq. 122]
has covariant
indices and
TiK
contravariant indices
and
they
also differ
in
their last
terms.
[90][Eqs.
123-125] together
form the
fully
covariant Ricci
tensor
which
Einstein
begins
re-
ducing
under the
assumption G
=
1,
so
that the
term containing
yKlgKl,
p
"drops
out"
("fällt
weg").
[Eq. 124]
reduces
to
[eq.
126],
and
[eq. 125]
to
[eq. 127].
[p.
35]
1
271(1
axjaxm
dXKdXm
a
4ax,
1
___
_4y~p
dx,
1
a7~
____ ____
--
___ ___
2axpLaxm~
1 ag1~
(agmp
4YKlYpaL ax1
-
ax,
axK
-
a
1
(~Z~
dgj~ d7~
dgmp
O7~
dg1~,
~\
1
N
c1g~~
dgmp
I
_____________ ______________ ________________ _____________ ______________ ______________ ________________--
4
~axm
ax1
+ a
-
axm
J
-
4~'~~\~X1
1
dYKp
ag~~
ax,
atm
[91]
[eq.
128]
i
m
[eq.
129]
[eq.
130]
[eq.
131]
[92]
[eq.
132]
[91][Eq.
128],
[eq.
130],
and
[eq. 131]
combined
give
the reduced
expression
for the Ricci
tensor
of
[p.
34].
[92]Expression [eq.
131]
is
expanded to
[eq.
132]
with the
help
of the results of
[p.
36].