eldorado.tu-dortmund.de/server/api/core/bitstreams/2d06ce7e-d3c2-476c-8cac-1570b903b219/content
Writing your Thesis with LateX
T(r,s+1)(M) with components Ki1···ir
j1···js;k := ∇kKi1···ir j1···js , where
∇kKi1···ir j1···js = ∂kK
i1···ir j1···js +
r∑︂ µ=1
Γ iµ kαK
i1···iµ−1αiµ+1···ir j1···js −
s∑︂ ν=1
ΓαkjνK i1···ir j1···jν−1αjν+1···js [...] ·wk⟩Symk
= 1
(k+ 1)!
k+1∑︂ i=1
⟨vi, v⟩perm
⟨v1,w1⟩ · · · ⟨v1,wk⟩ ...
. . . ...
ˆ︂⟨vi,w1⟩ · · · ˆ︂⟨vi,wk⟩ ...
. . . ...
⟨vk+1,w1⟩ · · · ⟨vk+1,wk⟩
= 1
(k+ 1)! perm
⟨v1, v⟩ ⟨v1,w1⟩ · · [...] implies
xm+1 =
m∑︂ ℓ=0
⌊ ℓ2⌋∑︂ k=0
m− ℓ+ 1 (m+ 1)k!
∑︂ I∈Nk
0 , |I|=ℓ
(︃ m+ 1
m− ℓ+ 1, i1, . . . , ik
)︃ Am−ℓAi1−1 · · ·Aik−1x0
=
⌊m+1 2 ⌋∑︂ k=0
1 k!
∑︂ I∈Nk
0 , |I|=m+1
(︃ m+ 1 i1, . . . , ik
)︃ Ai1−1 · · ·Aik−1x0 …
