I want to know the answer to the following question:
What concept investigates geometric elements that stay stable under group action?
All the background I'm provided with is that "Another application is differential Galois theory, which characterizes functions having antiderivatives of a prescribed form, giving group-theoretic criteria for when solutions of certain differential equations are well-behaved.u[›] Geometric properties that remain stable under group actions are investigated in (geometric) invariant theory.". Is that enough to answer the question?
Answer: yes