Estimado Dr. Crespin: siento no poder responder su pregunta: escapa a mi especialidad.

Atentamente: S. Urdaneta-Morales

I used 2 years ago a similar-if not identical as far as its looks is concerned!-  concave surface in order to realize a mesh of points with rational coordinates following a classical in numerical analysis algorithm,I am sure that beck then there was not an established name and probably neither today.So dear Dr.Crespin thiw is a good opportonity to become a godfather΄ασ α φαωορ πθτ ιντο υοθρ τερμ α ωαριατιον οφ α ςορδ ηαωινγ...Γρεεκ οριγιν!

Dear Professor  Karayannakis

Thanks for the information. I am not in a hurry to become father or godfather to the surface. But it would be interesting to see any results about curvature, principal directions, etc. and perhaps some intrinsic characterization.

If it has been used in numerical analysis, a reference will be appreciated.

I am ashamed of my ignorance of Greek language but in truth, and after transliterating, still am not sure of the meaning of the final statement.(as a favor pet into ... term a variation of a sort ... Greek origin???)

With best regards,

Daniel Crespin

Dear Daniel,never mind my bad+black humor.!..Yes, this surface probably has interesting (intrinsic?geometric?) properties that could illuminate the birth of a suitable  name for it(  maybe something more serious but along the lines of "cylindrical twist").By the way cylinder is a 100% Greek word..The verb bend is not and probably is not even Latin.

All my best

Dimitri K.

Not a bad name indeed!But since it can be bent in two ways with an suitable adjective in front could be  a more "accurate" description

"Viking Helmet" is evocative of wings

(i) melting cylinder

(ii) cylinder caterinary