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GEODESIC SPHERES AND BALLS OF THE HEISENBERG GROUPS

박지혜|박건|장창림
대한수학회 (The Korean Mathematical Society)|2010.01|대한수학회논문집 (Communications of the KMS)|제25권 제1호|pp. 83-96

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참고문헌

키워드

Heisenberg groupgeodesic spheregeodesic ball
주제분류수학

초록

Let H2n+1 be the (2n + 1)-dimensional Heisenberg group equipped with a left-invariant metric. In this paper we study the Gaussian curvatures of the geodesic spheres and the volumes of geodesic balls in H2n+1.

Abstract

Let H2n+1 be the (2n + 1)-dimensional Heisenberg group equipped with a left-invariant metric. In this paper we study the Gaussian curvatures of the geodesic spheres and the volumes of geodesic balls in H2n+1.

참고문헌 (12)

  1. J. Berndt, "Geometry of generalized Heisenberg groups and their Damak-Ricci harmonic extensions", Lecture Notes in Mathematics, 1598, pp.51~68 (1995)
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  3. P. Eberlein, "Geometry of 2-step Nilpotent Lie groups with a left invariant metric", Ann. Scient. Ecole Normale Sup., 27, pp.611~660 (1994)
  4. S. Gallot, "Riemannian Geometry" (1990), Springer-Verlag
  5. 장창림, "Conjugate points on the quaternionic Heisenberg group", 대한수학회지, 40(1), pp.61~72 (2003), 대한수학회
  6. C. Jang, "Conjugate points on 2-step nilpotent groups", Geom. Dedicata, 79, pp.65~80 (2000)
  7. A. Kaplan, "Riemannian nilmanifolds attached to Clifford modules", Geom. Dedicata, 11, pp.127~136 (1981)
  8. A. Kaplan, "On the geometry of groups of Heisenberg type", Bull. London Math. Soc., 15, pp.35~42 (1983)
  9. R. Kim, "On the geodesic spheres of the Heisenberg groups H3", pp.2003
  10. M. S. Raghunathan, "Discrete Subgroups of Lie Groups" (1972), Springer-Verlag
  11. G. Walschap, "Cut and conjugate Loci in two-step nilpotent Lie groups", Jour. of Geometric Analysis, 7, pp.343~355 (1997)
  12. T. J. Wilmore, "Riemannian Geometry" (1993), Oxford Univ. Press

관련 논문AI추천

BISECTORS IN THE HEISENBERG GROUP IGaoshun Gou, Ioannis D. Platis, Yue-Ping Jiang대한수학회 · 대한수학회보2023 · 제60권 제1호Geodesics on the K\"ahler cone of the Heisenberg group김준형, Ioannis D. Platis, Li-Jie Sun강원경기수학회 · 한국수학논문집2024 · 제32권 제4호Some translation surfaces in the 3-dimensional Heisenberg group윤대원, 이철우, Murat Kemal Karacan대한수학회 · 대한수학회보2013 · 제50권 제4호GEODESIC FORMULA OF A CERTAIN CLASS OF PSEUDORIEMANNIAN 2-STEP NILPOTENT GROUPS AND JACOBI OPERATORS ALONG GEODESICS IN PSEUDORIEMANNIAN 2-STEP NILPOTENT GROUPS박건, 장창림, B. Min영남수학회 · East Asian Mathematical Journal2010 · 제26권 제5호Differential geometric properties on the Heisenberg groupJoon-Sik Park대한수학회 · 대한수학회지2016 · 제53권 제5호Left-invariant minimal unit vector fields on a Lie group of constant negative sectional curvature이승훈대한수학회 · 대한수학회보2009 · 제46권 제4호

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