Abstract
In this chapter, V is a smooth real manifold, of dimension n = 2r, paracompact and endowed with an almost symplectic structure defined by a field F of alternating bilinear forms of maximal rank n = 2r in every point. If dF = 0, V is a symplectic manifold. It is equivalent to state that V has an almost complex structure (cf. Chapter 14, 3.2); to an almost complex structure there always corresponds an almost hermitian structure. Such a manifold is known to be orientable.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
