  The spintronic properties of curved nanostructures derived from
two-dimensional topological insulators (2DTI's) are explored theoretically with
density functional theory-based (DFT) calculations and tight-binding models. We
show that curved geometries make it possible to manipulate electron spins in
ways that are not available for planar 2DTI devices. We predict that, unlike
planar 2DTI devices, curved 2DTI-related nanostructures can function as highly
effective {\em two}-terminal spin filters even in the absence of magnetic
fields. We construct a generalization to curved geometries of our previous
tight binding model of the wide band gap planar 2DTI bismuthene on SiC. The
resulting model, applied to an ideal dome geometry with a free edge, is shown
to exhibit quantum spin Hall physics, including spin polarized edge states. The
model predicts nearly perfect spin filtering by the dome for a particular
two-terminal geometry in the absence of magnetic fields. Our DFT calculations
predict a Bi$_{105}$Si$_{105}$H$_{15}$ dome of bismuthene with adsorbed silicon
and hydrogen atoms to be stable. Our tight binding model, adjusted to match
density of states given by DFT calculations, predicts that the
Bi$_{105}$Si$_{105}$H$_{15}$ dome should exhibit quantum spin Hall physics and
very effective spin filtering in a two-terminal arrangement.
