Strange problem with tensor products

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I have recently run into a strange setup in a project I am working on. But I cannot for the life of me figure out what this type of object looks like physically nor how to work with it. I am VERY new to tensor calc but I am trying to solve Euler-Lagrange equation with

$L=m_am^bm^c\nabla_c\nabla_bm^a$

I would be happy throwing this into Mathematica but I am unsure what the object left of the $\nabla's$ is or should look like.