Theory of nematic and polar active fluid surfaces

We derive a fully covariant theory of the hydrodynamics nematic and polar active surfaces, subjected to internal external forces torques. study symmetries surfaces find that in addition 5 different types in-plane isotropic can be classified into polar, 2 pseudopolar, pseudonematic surfaces. give examples physical realisations we have identified. obtain expressions for equilibrium tensions, moments, torques acting on passive or surface. calculate entropy production rate using framework thermodynamics close constitutive equations with symmetries. instabilities confined flat planar-chiral layer deformable surface broken up-down symmetry.