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Living systems are chiral on multiple scales, from constituent biopolymers tolarge scale morphology, and their active mechanics is both driven by chiralcomponents and serves to generate chiral morphologies. We describe themechanics of active fluid membranes in coordinate-free form, with focus onchiral contributions to the stress. These generate geometric `odd elastic'forces in response to mean curvature gradients but directed perpendicularly. Asa result, they induce tangential membrane flows that circulate around maximaand minima of membrane curvature. When the normal viscous force amplifiesperturbations the membrane shape can become linearly unstable giving rise toshape instabilities controlled by an active Scriven-Love number. We describeexamples for spheroids, membranes tubes and helicoids, discussing the relevanceand predictions such examples make for a variety of biological systems from thesub-cellular to tissue level.

A Twist On Active Membranes: Odd Mechanics, Spontaneous Flows and Shape Instabilities