Small deformation of a liposome in a linear shear flow

Taking into account bending resistance and fluidity of the membrane, we calculate deformation of a vesicle of the lipid-bilayer membrane in a linear shear flow. Here it is assumed that the vesicle is spherical when the system is at rest and that the deformation is small because the flow is weak in comparison with the bending rigidity of the membrane. Our result includes Taylor's standard result on the drop in a linear shear flow as an exceptional case.