# 2 dimensional homogeneous riemannian manifold has constant sectional curvature

Why does 2 dimensional homogeneous riemannian manifold have constant sectional curvature? I have no idea. Any hints to get me thinking?

• Hint: Start by writing down the definition of a homogeneous manifold; then think if isometries preserve Gaussian curvature. – Moishe Kohan Jun 21 '17 at 2:57