Lie Algebroid Foliations and E(m)-dirac Structures
نویسندگان
چکیده
We prove some general results about the relation between the 1-cocycles of an arbitrary Lie algebroid A over M and the leaves of the Lie algebroid foliation on M associated with A. Using these results, we show that a E1(M)-Dirac structure L induces on every leaf F of its characteristic foliation a E1(F )-Dirac structure LF , which comes from a precontact structure or from a locally conformal presymplectic structure on F . In addition, we prove that a Dirac structure L̃ on M × R can be obtained from L and we discuss the relation between the leaves of the characteristic foliations of L and L̃. MSC (2000): 17B63, 17B66, 53C12, 53D10, 53D17.
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