  For inviscid fluid flow in any n-dimensional Riemannian manifold, new
conserved vorticity integrals generalizing helicity, enstrophy, and entropy
circulation are derived for lower-dimensional surfaces that move along fluid
streamlines. Conditions are determined for which the integrals yield constants
of motion for the fluid. In the case when an inviscid fluid is isentropic,
these new constants of motion generalize Kelvin's circulation theorem from
closed loops to closed surfaces of any dimension.
