I'm trying to find conditions for an endomorphism $L:TM\rightarrow TM$ verfying the condition

$$
\oint_{j,k,l} \left(\mathcal{T}_L\right)_{jm}^i \left(\mathcal{T}_L\right)_{kl}^m =  \left(\mathcal{T}_L\right)_{jm}^i \left(\mathcal{T}_L\right)_{kl}^m + \left(\mathcal{T}_L\right)_{km}^i \left(\mathcal{T}_L\right)_{lj}^m + \left(\mathcal{T}_L\right)_{lm}^i \left(\mathcal{T}_L\right)_{jk}^m= 0,
$$

where $\mathcal{T}_L$ denotes the Nijenhuis torsion of $L$ and a sum over $m$ is understood.

Assuming dim$(M)=3$,the system should have $n^3(n-1)/2 =_{n=3} 27 $ equations. So, there is a compact way (maybe the `Table` command mixed with `DSolve`) to write the 27 equations quickly in `Mathematica`? And does the programm help me and will it solve symbolicaly the system giving the endomorphism $L$ in function of some real parameters?

Thanks :)

Pd: The Nijenhuis torsion of $L$ is written in terms of $L_j^i$ and $\frac{\partial L_j^i}{\partial x^k}$, such as show eq. 5 https://arxiv.org/pdf/1405.5118.pdf