Speaker : Professor Yen-Chang Huang (Xin-Yang Normal University, Henan)
Title : The existence of envelope curve in the model case of pseudohermitian manifolds.
Time : 2018-02-23 (Fri) 11:00 - 12:00
Place : Seminar Room 617, Institute of Mathematics (NTU Campus)
Abstract: In general, it is impossible to find a curve which is an envelope of a family of lines in the 3-dimensional Euclidean space due to the over-determined differential equations. Regard the 3D-Heisenberg group as a flat model of the pseudohermitian manifolds, we show the necessary and sufficient condition for the existence of horizontal envelopes and some examples. We also show a method to construct horizontal envelopes from the given ones, and characterize the solutions satisfying the construction. The same method can be generalized to the Heisenberg group of higher dimensions.