It is shown that the curvature bounded above (resp. below) in the sense of Alexandrov is equivalent to the curvature bounded above (resp. below) in the sense of Busemann if and only if the sum of adjacent average angles is at least (resp. at most) $\pi$.
Alexandrov curvature, Busemann curvature, average angles
"On the equivalence of Alexandrov curvature and Busemann curvature,"
Turkish Journal of Mathematics: Vol. 41:
1, Article 19.
Available at: https://journals.tubitak.gov.tr/math/vol41/iss1/19