Moduli Space of Timwe-like Pseudo Circles in R13

다국어 초록 (Multilingual Abstract)

It is of great importance to classify all kinds of hypersurface in different space forms. In this paper, we focus on the hypersurfaces foliated by time-like pseudo circles. In order to complete the classification, we study the moduli space 23 of time-like pseudo circles in 13. Firstly, We build the moduli space 23 of time-like pseudo circles in 13 which is definitely a Riemannian manifold. Secondly, we build Riemannian metric, Riemannian connections in 23 and prove that those are M̈bius invariant. Thirdly, up to M̈bius transformation, all the geodesics in 23 are determined to form a one-parameter family of time-like pseudo circles on a generalized helicoid in space form 13(1), 13(−1),13(0), resp. Moreover, we show that mean curvature of those hypersurfaces are zero in three space forms respectively. Finally by software Mathematica and Jreality, we show some special hypersurfaces foliated by time-like pseudo circles.

목차 (Table of Contents)

• Abstract
• 1. Introduction
• 2. Moduli Space of Time-like Pseudo Circles in 3
• 3. Geodesics on Moduli Space 3
• 3.1. {′(),′()} are Linearly Dependent
• 3.2. {′(),′()} are Linearly Independent
• Acknowledgment
• References