Differential geometry is the application of differential calculus in the setting of smooth manifolds (curves, surfaces and higher dimensional examples). Modern differential geometry focuses "geometric structures" on such manifolds, such as bundles and connections; for questions not concerning such ...
Suppose $f:M \to N$ is a smooth map between complete Riemannian manifolds of the same dimension. Suppose $Df(m_0)$ is invertible, and $n$ is a point close to $f(m_0)$. Can we perform Newton iteration ...