Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (3): 845-855.

• Articles • Previous Articles    

Symplectic Vector Fields on Two Types of Special Symplectic Supermanifolds

 WANG Bao-Qi1, ZENG Hui2   

  1. 1.School of Mathematical Science, Xinjiang Normal University, Urumq 830054;2.Department of Mathematics and Information Technology, Xinjiang Educational Institute, Urumq 830043
  • Received:2007-04-23 Revised:2010-08-24 Online:2011-06-25 Published:2011-06-25
  • Supported by:

    新疆维吾尔自治区教育科学计划青年教师培育基金(XJEDU2009S67)资助

Abstract:

In this paper, an operator η is defined in the left A module DerA on symplectic supermanifoldM = (e, A) of dimension (0, n). Two sufficient and necessary conditions are given for vector fields on M being symplectic vecter fields, and some identities about the operator η are obtianed. Furthermore, three decision conditions are given to judge symplectic vector fields on cotangent supermanifold T*(M) = (e, S(DerA)), and their equivalences are proved.

Key words: Symplectic supermanifold of dimension (0, n), Cotangent supermanifold T* (M) =(e, S(DerA)), Operator η, Symplectic vecter field.

CLC Number: 

  • 34B05
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