6 6 D O C U M E N T 8 1 M A R C H 1 9 2 1
If (negative per Wirtinger), then
,
.
Weyl’s invariant is
correct.[4]
I wanted to work on a few problems of rel[ativity] th[eory]. Would you be so
kind and grant me some of your time? I am mainly thinking of the questions: If
, and is regular and throughout finitude, is the manifold then
necessarily Euclidean? I believe a paper by Lipschitz may be applicable to this
question.[5] Another question: whether there is such a thing as a closed geodesic
worldline.[6]
I plan to write a book about the th. of rel. Also scientifically elaborating the
mathematical aspect. It would be good if I could take my Habilitation degree here
(until Palestine).[7] Would you provide me with assistance?
Prof. von Mises is a magnificent person and one could talk about it with him.[8]
With cordial regards, yours,
J. Grommer.
Besides, it does not seem right to me to confine oneself only to the second deriva-
tives, if only the ratios of the ’s play a part. The additional condition could also
contain higher derivatives.
81. To Alfred Kerr[1]
[Berlin,] 7 March 1921
Dear Mr. Kerr,
I hope your wife[2] is feeling well and your child[3] is in nondenominational
bliss.[4] You had barely left when I received a letter from a rabbi who was supposed
to sway me with cunning words into entering the religious community;[5] but Jeho-
vah will stand by his disloyal son, that he stay firm.[6] – I thank you cordially for
sending the books,[7] which I already relished dipping into. I am reminded of a
Riklm
1
2
-- -
xk xm
2
gil
… + = Riklm g =
Riklm
1
2
-- - gil
mk
gim
kl
– gkm
il
gkl
im
– +
3
4
------(gil
k m
gim
k l
– – + + =
gkm
i l
gkl
i m
)
1
4
------ gilgkm gimgkl – + – +
Rkm g Rkm
km
--------
3
2 2
-------- -
k m
–
gkm
2
-------- g . + – + =
R g
R
---
3
2
-----
il
gil
3
2
3
-------- -
m
m
– + =
Rik 0 = gik g 0 =
gik