Flat circle bundles, pullbacks, and the circle made discrete.
Homotopy theory and circle actions on symplectic manifolds
Introduction
Unduloids and their geometry
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.
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