Answer
"Eka-manganese" refers to Technetium (Tc).
Work Step by Step
The prefix "-eka," as mentioned, is used by Mendeleev to predict the unknown element that is one row below the mentioned element, as in the case of "eka-silicon."
Therefore, to find the element "eka-manganese," we would look at the periodic table and identify the element that is below manganese.
That element is Technetium (Tc).