Before revision:  In general, the interior angles of geodesic triangles can sum up to \pi like in Euclidean/Mahalanobis  geometry, or exhibit either angle excesses or angle defects.
After revision:  In general, the interior angles of geodesic triangles can sum up to \pi like in Euclidean/Mahalanobis flat geometry, or exhibit either angle excesses or angle defects.