From Sudopedia, the free Sudoku reference guide
Locally minimal
From Sudopedia
A Sudoku puzzle is locally minimal when removing any of its givens results in a puzzle that has multiple solutions.
Locally minimal is not the same as minimal. The same solution grid can contain a puzzle with fewer givens, but that puzzle will contain at least one given which does not belong to the locally minimal puzzle.
A puzzle is symmetrically minimal when it cannot be reduced within the symmetry restrictions.
