Real hypersurfaces of $e$-$(J^4=1)$-Kaehler manifolds

Abstract

[EN]We study the geometry of real hypersurfaces immersed in e-(J⁴ = 1)-Kaehler manifolds, a class of semi-Riemannian manifolds that generalizes both classical Kaehler and para-Kaehler structures. After recalling the fundamental definitions and properties of e-(J⁴ = 1)-Kaehler manifolds, we derive the induced geometric structure on a real hypersurface, considering both non-degenerate and degenerate (null) cases with respect to the semi-Riemannian metric. We characterize the integrable distributions arising on such hypersurfaces in terms of their second fundamental forms and shape operators, and identify conditions that distinguish CR-type substructures within the hypersurface. Our results extend classical submanifold theory to the broader context of e-(J⁴ = 1)-geometry, highlighting the interplay between the ambient complex-product structure and the intrinsic geometry of hypersurfaces.