Applications of harmonic morphisms to gravity

We introduce the notion of gravity coupled to a horizontally conformal submersion as a modification of the well-known concept of gravity coupled to a harmonic map, thus obtaining a coupled gravity system with a more geometric flavor. By using integral techniques we determine the necessary conditions for coupling and cosmological constants. Finally, in the context of higher dimensional gravitation theory, we show that harmonic morphisms provide a natural ansatz to trigger spontaneous splitting and reduction of the gravity system coupled to a harmonic map on (4+D) (D⩾1) dimensional space–times.