Speaker: M.B. Skopenkov (NRU Higher School of Economics, Institute for Information Transmission Problems RAS, Moscow, Russia).
Time: 2021-11-01 16:00 Novosibirsk time (12:00 Moscow time, 17:00 Beijing time).
Abstract: Motivated by applications in engineering, we provide characterizations of surfaces which are enveloped by a one-parametric family of congruent cones. As limit cases we also address developable surfaces and ruled surfaces. The characterizations are higher-order nonlinear PDEs generalizing the ones by Gauss and Monge. In the process we reconstruct the positions of the cones for a given envelope. The methodology is based on a model of Laguerre geometry, which transforms an envelope to a surface containing a special conic through each point. Most of the talk is explained in figures and is accessible to undergraduate students.
This is joint work with Pengbo Bo, Michael Barton, Helmut Pottmann.
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