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On 4‐dimensional Lorentzian affine hypersurfaces with an almost symplectic form
Author(s) -
Szancer Michal,
Szancer Zuzanna
Publication year - 2020
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201900269
Subject(s) - mathematics , symplectic geometry , affine transformation , pure mathematics , rank (graph theory) , affine geometry of curves , affine combination , integer (computer science) , order (exchange) , symplectic group , mathematical analysis , combinatorics , finance , computer science , economics , programming language
In this paper we study 4‐dimensional affine hypersurfaces with a Lorentzian second fundamental form additionally equipped with an almost symplectic structure ω. We prove that the rank of the shape operator is at most one ifR k · ω = 0 or∇ k ω = 0 for some positive integer k . This result is the final step in a classification of Lorentzian affine hypersurfaces with higher order parallel almost symplectic forms.