  A general geometrical scheme is presented for the construction of novel
classical gravity theories whose solutions obey two-sided bounds on the
sectional curvatures along certain subvarieties of the Grassmannian of
two-planes. The motivation to study sectional curvature bounds comes from their
equivalence to bounds on the acceleration between nearby geodesics. A universal
minimal length scale is a necessary ingredient of the construction, and an
application of the kinematical framework to static, spherically symmetric
spacetimes shows drastic differences to the Schwarzschild solution of general
relativity by the exclusion of spacelike singularities.
