Abstract: In this document, we study the interaction between different geometric structures defined on the generalized tangent bundle TM := T M T *M -> M. Specifically, we study various generalized polynomial ?-structures J with respect to different metrics G on TM when J 2 = ?Id, G(J ·, J ·) = ?G(·, ·), for ?, ? ? {+1, -1}. Besides, we study the commutation or anti-commutation of generalized polynomial structures, showing that a generalized Kähler structure can be understood as a pair of commuting generalized almost complex structures.

Authorship

Download reference