Does there exist a known example of Riemannian manifold who its sectional curvature admit both zero and positive values?

Question

Does there exist a known example of Riemannian manifold who its sectional curvature admit both zero and positive values ?

Answer 1

For $2$-manifolds, the sectional curvature is the Gauss curvature, see

Sectional Curvature, Gauss curvature

Theorem (From Do Carmo's book, p. 282, see below): Let $S\subseteq \mathbb{R}^3$ be a connected, regular, compact, orientable surface which is not homeomorphic to a sphere. Then there are points on $S$ where the Gaussian curvature is positive, negative, and zero.

Proof: Compact surface with Gaussian curvature is positive, negative, and zero

See here for a nice example on the $2$-torus.