Colloquium / Seminars
Topic:The Differential Geometry of Curves in Space Forms of Pseudo-Hermitian Manifolds
Speaker:Prof. Yen-Chang Huang
(Dept. of Applied Mathematics, National University of Tainan)Date time:Mar. 19, 2024 14:00 - 15:00
Venue:SA223
Abstract:
Abstract
The exploration of submanifolds in spaces of constant sectional curvature is fundamental to Differential Geometry. Since 2015, significant progress has been achieved by Chiu-Huang-Lai and Chiu-Ho, who established the Fundamental Theory of Curves and Surfaces in the Heisenberg group H₁ and the CR sphere S³ respectively. Their research resulted in the identification of a comprehensive set of geometric invariants, specifically curvatures for curves and surfaces. Acting as pseudo-Hermitian manifolds, H₁ and S³ represent special cases of CR manifolds, embodying zero and positive constant sectional curvatures, respectively. Recently, Pak Tung Ho (Tamkang University) and I have extended our research to include the final model case—the constant negative sectional curvature—in the product space consisting of a unit 2-sphere and the real line. This presentation will provide a concise review of our previous findings and will concentrate on developing geometric invariants in this product space. Furthermore, I will explore the proof of the Fundamental Theorem of Curves, supported by a series of intriguing examples.Download:Talk_1130319.pdf
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