Unduloids and their geometry

Mariana Hadzhilazova, Ivailo M. Mladenov, John Oprea

Address. M. Hadzhilazova and I. M. Mladenov, Institute of Biophysics
Bulgarian Academy of Sciences, Acad. G. Bonchev Str.
Bl. 21, 1113 Sofia, Bulgaria
J. Oprea, Department of Mathematics, Cleveland State University
Cleveland, OH 44115, USA

E-mail: murryh@obzor.bio21.bas.bg



Abstract. In this paper we consider non-compact cylinder-like surfaces called unduloids and study some aspects of their geometry. In particular, making use of a Kenmotsu-type representation of these surfaces, we derive explicit formulas for the lengths and areas of arbitrary segments, along with a formula for the volumes enclosed by them.

AMSclassification. 53A05, 53C42, 53-04, 49Q10.

Keywords. Mean curvature, unduloid.