본문 바로가기
KERD
논문KCI 등재

Helicoidal Killing fields, helicoids and ruled minimal surfaces in homogeneous three-manifolds

0

조회

0

다운로드

0

인용

0

참고문헌

키워드

주제분류수학

초록

We provide definitions for the helicoidal Killing field and the helicoid in arbitrary three-manifolds, and investigate helicoids and ruled minimal surfaces in homogeneous three-manifolds, mainly in $\rm{SL_2}\mathbb R$ and Sol(3). In so doing we finish our classification of ruled minimal surfaces in homogeneous three-manifolds with the isometry group of dimension 4.

Abstract

We provide definitions for the helicoidal Killing field and the helicoid in arbitrary three-manifolds, and investigate helicoids and ruled minimal surfaces in homogeneous three-manifolds, mainly in $\rm{SL_2}\mathbb R$ and Sol(3). In so doing we finish our classification of ruled minimal surfaces in homogeneous three-manifolds with the isometry group of dimension 4.

참고문헌 (13)

  1. M. Bekkar, "Helicoids and axially symmetric minimal surfaces in 3-dimensional homogeneous spaces", Differ. Geom. Dyn. Syst., 9, pp.21~39 (2007)
  2. S. Cartier, "Noether invariants for constant mean curvature surfaces in 3-dimensional homogeneous spaces", arXiv:1303.6391v1, ~
  3. B. Daniel, "Isometric immersions into 3-dimensional homogeneous manifolds", Comment. Math. Helv., 82(1), pp.87~131 (2007)
  4. S. Fujimori, "Spacelike mean curvature one surfaces in de Sitter 3-space", Comm. Anal. Geom., 17(3), pp.383~427 (2009)[DOI]
  5. Y. W. Kim, "Helicoids in <TEX>${\mathbb{S}}^2{\times}{\mathbb{R}}$<", TEX> and <TEX>${\mathbb{H}}^2{\times}{\mathbb{R}}$<, Pacific J. Math., pp.2009, 242(2)[DOI]
  6. Y. W. Kim, "Helicoidal minimal surfaces in <TEX>${\mathbb{H}}^2{\times}{\mathbb{R}}$<", TEX>, 2012, pp.86(1), 135~149
  7. M. Kokubu, "On minimal surfaces in the real special linear group SL(2,R)", Tokyo J. Math., 20(2), pp.287~297 (1997)[DOI]
  8. H. B. Lawson Jr., "Complete minimal surfaces in <TEX>$S^3$<", TEX>, 1970, pp.92, 335~374
  9. R. Lopez, "Surfaces in <TEX>$Sol_3$<", TEX> space foliated by circles, 2013, pp.64(3-4), 319~330
  10. J. Plehnert, "Constant mean curvature k-noids in homogeneous manifolds", Illinois J. Math., 58(1), pp.233~249 (2014)
  11. H. Shin, "Ruled minimal surfaces in the three-dimensional Heisenberg group", Pacific J. Math., 261(2), pp.477~496 (2013)[DOI]
  12. H. Shin, "Ruled minimal surfaces in the Berger sphere", Differential Geom. Appl., 40, pp.209~222 (2015)[DOI]
  13. R. Souam, "Totally umbilic surfaces in homogeneous 3-manifolds", Comment. Math. Helv., 84(3), pp.673~704 (2009)

관련 논문AI추천

이 간행물의 다른 논문 (17건)