Conformal transformations of vesicle shapes

Phase diagrams and shape transformations of toroidal vesicles

Shapes of vesicles with toroidal topology are studied in the context of curvature models for the membrane. For two simplified curvature models, the spontaneous-curvature (SC) model and the bilayer-couple (BC) model, the structure of energy diagrams, sheets of stationary shapes and phase diagrams are obtained by solving shape equations for axisymmetric shapes. Three different sheets of axisymmet...

On Infinitesimal Conformal Transformations of the Tangent Bundles with the Generalized Metric

Let  be an n-dimensional Riemannian manifold, and  be its tangent bundle with the lift metric. Then every infinitesimal fiber-preserving conformal transformation  induces an infinitesimal homothetic transformation on .  Furthermore,  the correspondence   gives a homomorphism of the Lie algebra of infinitesimal fiber-preserving conformal transformations on  onto the Lie algebra of infinitesimal ...

A Characterization of the Infinitesimal Conformal Transformations on Tangent Bundles

Vesicles of toroidal topology.

We consider Quid vesicles of toroidal topology. Minimization of the curvature energy at fixed volume and area leads to three difterent branches of axisymmetric shapes. By using conformal transformations, we identify a large region of nonaxisymmetric shapes in the phase diagram. For vanishing spontaneous curvature, the ground state is twofold degenerate in this region and corresponds to zero pre...

On conformal transformation of special curvature of Kropina metrics

      An important class of Finsler metric is named Kropina metrics which is defined by Riemannian metric α and 1-form β  which have many applications in physic, magnetic field and dynamic systems. In this paper, conformal transformations of χ-curvature and H-curvature of Kropina metrics are studied and the conditions that preserve this quantities are investigated. Also it is shown that in the ...

Bogomol’nyi decomposition for vesicles of arbitrary genus

We apply the Bogomol’nyi technique, which is usually invoked in the study of solitons or models with topological invariants, to the case of elastic energy of vesicles. We show that spontaneous bending contribution caused by any deformation from metastable bending shapes falls in two distinct topological sets: shapes of spherical topology and shapes of non-spherical topology experience respectiv...