Earticle

초록

영어

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 𝐐23 of time-like pseudo circles in 𝐑13. Firstly, We build the moduli space 𝐐23 of time-like pseudo circles in 𝐑13 which is definitely a Riemannian manifold. Secondly, we build Riemannian metric, Riemannian connections in 𝐐23 and prove that those are M𝑜̈bius invariant. Thirdly, up to M𝑜̈bius transformation, all the geodesics in 𝐐23 are determined to form a one-parameter family of time-like pseudo circles on a generalized helicoid in space form 𝐌13(1), 𝐌13(−1),𝐌13(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

Abstract
 1. Introduction
 2. Moduli Space of Time-like Pseudo Circles in 𝐑3𝟏
 3. Geodesics on Moduli Space 𝐐3𝟐
  3.1. {𝒖′(𝟎),𝒗′(𝟎)} are Linearly Dependent
  3.2. {𝒖′(𝟎),𝒗′(𝟎)} are Linearly Independent
 Acknowledgment
 References

저자

• Linyuan Fan [ School of Statistics, Capital University of Economics and Business, Beijing, China ]

참고문헌

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간행물

표지보기 관심저널 등록

• 간행물명

  International Journal of Signal Processing, Image Processing and Pattern Recognition

• 간기

  격월간

• pISSN

  2005-4254

• 수록기간

  2008~2016

• 십진분류

  KDC 505 DDC 605