The variational theory of perfect fluid with intrinsic hypermomentum in space-time with nonmetricity

The variational theory of the perfect fluid with an intrinsic hypermomentum is developed. The Lagrangian density of such fluid is stated and the equations of motion of the fluid and the evolution equation of the hypermomentum tensor are derived. The expressions of the matter currents of the fluid (the metric stress-energy 4-form, the canonical energy-momentum 3-form and the hypermomentum 3-form) are obtained.