Generalizing axioms of $r$-planes and $r$-spheres on Riemannian and Kähler manifolds

Cristina Levina, Sérgio Mendonça

The famous theorems of Cartan, related to the axiom of $r$-planes, and Leung-Nomizu about the axiom of $r$-spheres were extended to Kähler geometry by several authors. In this pape…