GENERATION METHOD FOR SOLUTIONS OF EINSTEIN-MAXWELL EQUATIONS AND ITS GEOMETRICAL BACKGROUND JAN NOVOTN\'Y AND JAN HORSK\'Y Abstract. Geometrical facts are presented supporting the conjecture on the connection between gravity and electromagnetism, leading to a new method finding classes of solutions of Einstein-Maxwell equations. On this basis, the conjecture in question is more precisely formulated. Keywords. Generation method, Einstein-Maxwell equations, Killing vectors. MS classification. 83C50.