Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (4): 816-822.

• Articles • Previous Articles     Next Articles

Reachable Sets for |Heisenberg Group H2 with sub-Lorentzian Metric

 HUANG Ti-Ren1,2, YANG Xiao-Ping3   

  1. 1.Department of Mathematics, Zhejiang |Sci-Tech University, Hangzhou 310018|2.School of Mathematical Sciences, USTC, Hefei 230022|3.Department of Applied Mathematics, Nanjing University of Science &|Technology, Nanjing 2100941
  • Received:2012-10-08 Revised:2013-08-06 Online:2014-08-25 Published:2014-08-25
  • Supported by:

    国家自然科学基金(10771102)和安徽省高等学校优秀青年人才基金(2010SQRL169)资助

Abstract:

Let H2 be the Heisenberg  group in R5 and D be a bracket generating left invariant distribution with a Lorentzian metric. Let reachable sets I+(0)(resp.J+(0)) be the chronological(resp.causal) future of origin. In this paper, we prove that I+(0) is open and J+(0) is closed for Heisenberg group H2 with sub-Lorentzian metric, which are similar results as in Lorentzian manifolds.

Key words: Reachable sets, Heisenberg group, sub-Lorentzian metric

CLC Number: 

  • 58E10
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