Equivolumetric tubular solids for volume-preserving bend of cylinders

We present the equivolumetric tubular solid which is a model of volume-preserving bend of right cylinders. The equivolumetric tubular solid is a special class of tubular solids which are the generalization of pipe solids or normal ringed solid. For a given spine curve, the volume of the sectorial tube of a pipe solid suffers distortion due to the curvature of the spine curve. The radial distance function of the equivolumetric tubular solid is elaborately chosen so as to compensate for this curvature effect. We also investigate the algebraic property of the equivolumetric torus which is an equivolumetric tubular solid with circular spine curve. Finally, we prove that the equivolumetric tubular surface is a limit of an equivolumetric offset surface of the pipe surface along the spine curve.