418. Calculations on Back Pages of Travel Diary
[ca. 9–22 January
1923][1]
[p. 51]

∂xτ
-------( gμνgμν) 0= gμα
∂gμν
∂xτ
-----------gνσ
∂gνσ
-----------gμνxτ∂ –=
∂gνσ
∂xσ
----------- =
∂gασ
∂xτ
-----------δν -
α gαμgσν-----------μν
∂g
∂xτ
–=
gαμgσν
μτ
ν
ντ
μ
+ –=
∂gασ
∂xτ
----------- - gαμΓμτ σ gσνΓντα =
∂gασ
∂xσ
----------- - gαμΓμσ σ gσνΓνσα =
∂Aν
∂xβ
-------- - Γαβ
ν
+
BβCν
Inv Tens. =
Γαβ ν AαBβCν Inv.
∂Aν
∂xβ
--------BβCν - –=
Γαβ'Aα'Bβ'Cν' ν Inv.
∂Aν'
∂xβ'
--------- -Bβ'Cν' –=
∂Aν
∂xβ
-------- - Γαβ
ν
+
BβCν
∂An'
∂xb'
--------- -
Γab'Aa n
'+
Bb'Cn'
=
∂xβ
∂xb'
-------- -

∂xβ
------- -
∂An
∂xν
-------- -
dxν
' ∂x
∂xν
--------Aν-n

∂xβ
∂xb'
------------------------Aν -
∂2xn'
∂∂ ∂xb'
--------------------------nAν∂'x∂-βx∂
∂xν ∂xβ
+
Γαβ
ν AαBβCν
∂xβ
∂xb'
------------------------AνBb'Cn'
-
∂2xn'
∂∂
Γab'Aa'Bb'Cn'n
+ =
∂x
∂xa'
--------Aa'-ν
Γαβ ν
∂xα
∂xa'∂xb'
------------------------ -
∂xβ
-
∂xn-'
∂xν
∂xβ
∂xb'∂xa'
-------------------------------- -
∂xν
-
∂2xn'
∂∂
Γab n '+ =
'∂x ∂x
∂xτ
-------------------------ρ-a-b
'
∂xσ
∂x
∂xn'
Γστ ρ
∂2xn'
xσ∂xn' ∂∂
------------------------
∂xρ
- Γab'…An' n
δνβδνσ ∂xν
∂xn'∂xβ
--------------- -

-
' ∂x
∂xν
---------n
+ =
Γστ ρ
∂2xn'
∂∂
----------------An' Γab'An'∂xn-'Aρ n
∂xρ
-------- + =

∂x
∂xa'
'=aA-ρ--------
dAν δAνVektor
∂Aν
∂xβ
-------- - Γαβ ν + dxβ =
δAν Γαβ ν Aαdxβ –=
dAν
∂Aν
∂xβ
--------dxβ - =
[eq. 1]
0
0
[2]
Previous Page Next Page