In mathematics|lang=en terms the difference between invariant and invariantly
is that
invariant is (mathematics) unaffected by a specified operation (especially by a transformation) while
invariantly is (mathematics) in a manner that is invariant; unaffected by some operation.
As an adjective invariant
is not varying; constant.
As a noun invariant
is an invariant quantity, function etc.
As an adverb invariantly is
(mathematics) in a manner that is invariant; unaffected by some operation.