DOI QR코드

DOI QR Code

CONSTANT CURVATURES AND SURFACES OF REVOLUTION IN L3

  • Kang, Ju-Yeon (Department of Mathematics, Chonnam National University) ;
  • Kim, Seon-Bu (Department of Mathematics, Chonnam National University)
  • Received : 2015.08.31
  • Accepted : 2016.02.12
  • Published : 2016.03.25

Abstract

In Minkowskian 3-spacetime $L^3$ we find timelike or spacelike surface of revolution for the given Gauss curvature K = -1, 0, 1 and mean curvature H = 0. In fact, we set up the surface of revolution with the time axis for z-axis to be able to draw those surfaces on standard pictures in Minkowskian 3-spacetime $L^3$.

Keywords

Minkowskian 3-spacetime;surface of revolution;minimal timelike surface;maximal spacelike surface;constant Gaussian curvature

References

  1. Paul Ehrlich and Seon-Bu Kim, Differential Geometry in Euclidean and Minkowskian spaces, Kyung Moon Sa, New Jersey, 2013.
  2. Ju-Yeon Kang, On Surfaces of revolution of constant curvatures in Minkowski 3-space, Thesis of M.S. degree in Math. Chonnam.National University, 2013.
  3. Wolfgang Kuhnel, Differential Geometry: Curves-Surfaces-Manifolds, Student mathematical library, Providence, RI: American Mathematical Society, 16 (2002)
  4. Richard S. Millman and George D. Parker, Elements of Differential Geometry, Prentice-Hall, New Jersey, 1977.
  5. Barrett O'Neill, Elementary Differential Geometry, Academic Press, New York, 1966.
  6. Andrew Pressley, Elementary Differential Geometry, second edition, 2010