Two inequations of curvature tensor.

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How to get the two inequations 1 and 2.

And I think the RHS of 1.4.2 should be $$ \Delta(\nabla R_m)+2R_m*(\nabla R_m) $$

Besides, What's the define of $A*B$?

Soryy for my lazy, the below picture is from the 191th page of paper

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