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

Author

Listed:
  • Elisabetta Barletta

    (Dipartimento di Matematica, Informatica ed Economia, Università degli Studi della Basilicata, 85100 Potenza, Italy)

  • Sorin Dragomir

    (Dipartimento di Matematica, Informatica ed Economia, Università degli Studi della Basilicata, 85100 Potenza, Italy)

  • Francesco Esposito

    (Dipartimento di Matematica e Fisica Ennio De Giorgi, Università del Salento, 73100 Lecce, Italy)

Abstract

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 2 s , 0 < s < n , is locally biholomorphically homothetic to an indefinite complex Hopf manifold C H s n ( λ ) , 0 < λ < 1 , equipped with the indefinite Boothby metric g s , n .

Suggested Citation

  • Elisabetta Barletta & Sorin Dragomir & Francesco Esposito, 2021. "On the Canonical Foliation of an Indefinite Locally Conformal Kähler Manifold with a Parallel Lee Form," Mathematics, MDPI, vol. 9(4), pages 1-15, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:333-:d:495188
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    References listed on IDEAS

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    1. K. L. Duggal, 1990. "Space time manifolds and contact structures," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 13, pages 1-9, January.
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