Morse–Bott function

Summary

A Morse–Bott function is a smooth function whose critical points form submanifolds, and which is nondegenerate in the directions normal to these submanifolds. It generalizes a Morse function, whose critical submanifolds are points. Raoul Bott introduced the notion for functions with symmetry, whose critical points come in families. An example is the energy on spaces of paths in a symmetric space.