Riemannian submersion

A **Riemannian submersion** is a specific type of mathematical structure that arises in differential geometry. It involves two Riemannian manifolds and a smooth map between them that preserves certain geometric properties. More formally, let \( (M, g_M) \) and \( (N, g_N) \) be two Riemannian manifolds, where \( g_M \) and \( g_N \) are their respective Riemannian metrics.