\[\star E=\pm E,\mathrm{d}E=0\Longrightarrow \star\mathrm{d}\star E=0\]

\[g_{p\left(b \right)}\left(\Pi_Cv,\Pi_Cw \right)=g_{p\left(a \right)}\left(v,w \right)\]

\[D\left(p\parallel q \right):=\psi\left(p \right)+\varphi\left(q \right)-\theta^i\left(p \right)\eta_i\left(q \right)\]

\[R\left(X,Y,Z \right):=\nabla _X\left(\nabla _YZ \right)-\nabla _Y\left(\nabla _XZ \right)-\nabla _{\left[X,Y \right]}Z\]

\[Xg\left(Y,Z \right)=g\left(\nabla _XY,Z \right)+g\left(Y,\nabla ^*_XZ \right)\]

可積分性と熱化の関係、微分ガロア群が使えそうな気がするのですがどうなんでしょ

$a_k=2k+1$
$a_1=3,a_2=5,a_3=7,a_4=9,a_5=11\cdot$

$b_k=a_k-min(k,3)$
$b_1=2,b_2=3,b_3=4,b_4=6,b_5=8\cdot$

$\sum _{k,l=1}^2h_{k\bar{l}}\mathrm{d}z_k \mathrm{d}\bar{z}_l$
$=
\sum _{k,l=1}^4\left(\iota_{sym}\left[ h\right] \right)_{kl}\mathrm{d}x^k \mathrm{d}x^l$

$SHerm=SHerm_++SHerm_-$
$SHerm:=$
$\left\{h\in M_2\mathbb{C}~\big|~h=h^\dagger,~det\left[h \right]=1 \right\}$
$Herm_{\pm}:=$
$=\left\{\left( \begin{array}{cc} a & b \\ \bar{b} & d \end{array} \right) \in M_2\mathbb{C}~\big|~~\pm a>0,~\pm d>0,~a\times d\geq 1,~\left|b \right|=\sqrt{a\times d- 1} \right\}$

もの凄く幼稚で初等的なことを証明した(っぽい)のですが、正しいことが確認出来たらトゥートするかも

$\hat{F}_{\mu\nu}:=\mathrm{i}\left[\hat{\nabla }_\mu,\hat{\nabla }_\nu \right]$

${\displaystyle {\text{Ext}}_{A\otimes _{k}A^{op}}^{*}(A,M)} ={\displaystyle HH^{*}(A,M)}$

$A:=dist\left(\vec{0}_\odot,\vec{0}_\oplus \right)$
\[S=\frac{\sigma T_\odot^4\times 4\pi R_\odot^2}{4\pi A^2}\]

\[{R_{i\bar{j}k}}^l =\partial_i\Gamma^l_{\bar{j}k} - \partial_{\bar{j}}\Gamma^l_{ik}
+\Gamma^n_{\bar{j}k} \Gamma^l_{in} -\Gamma^n_{ik}\Gamma^l_{\bar{j}n}.\]

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