On the Canonical Foliation of an Indefinite Locally Conformal Kähler Manifold with a Parallel Lee Form

We study the semi-Riemannian geometry of the foliation F of an indefinite locally conformal Kähler (l.c.K.) manifold M, given by the Pfaffian equation ω=0, provided that ∇ω=0 and c=∥ω∥≠0 (ω is the Lee form of M). If M is conformally flat then every leaf of F is shown to be a totally geodesic semi-Ri...

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Bibliographic Details
Published in:Mathematics (Basel) 2021-02, Vol.9 (4), p.333
Main Authors: Barletta, Elisabetta, Dragomir, Sorin, Esposito, Francesco
Format: Article
Language:English
Subjects:
Geometry
Hyperspaces
indefinite Boothby metric
indefinite Hopf manifold
indefinite locally conformal Kähler manifold
indefinite Vaisman manifold
Lee form
Lee vector field
Mathematics
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Summary:We study the semi-Riemannian geometry of the foliation F of an indefinite locally conformal Kähler (l.c.K.) manifold M, given by the Pfaffian equation ω=0, provided that ∇ω=0 and c=∥ω∥≠0 (ω is the Lee form of M). If M is conformally flat then every leaf of F is shown to be a totally geodesic semi-Riemannian hypersurface in M, and a semi-Riemannian space form of sectional curvature c/4, carrying an indefinite c-Sasakian structure. As a corollary of the result together with a semi-Riemannian version of the de Rham decomposition theorem any geodesically complete, conformally flat, indefinite Vaisman manifold of index 2s, 0
ISSN:2227-7390
2227-7390
DOI:10.3390/math9040333