Splitting Parabolic Manifolds

Preprint English OPEN
Kalka, Morris; Patrizio, Giorgio;
  • Subject: Mathematics - Complex Variables
    arxiv: Mathematics::Complex Variables

We study the geometric properties of complex manifolds possessing a pair of plurisubharmonic functions satisfying Monge-Amp\`ere type of condition. The results are applied to characterize complex manifolds biholomorphic to $\C^{N}$ viewed as a product of lower dimension... View more
  • References (9)

    [1] E. Bedford and M. Kalka, Foliations and Complex Monge-Amp`ere Equations, Comm. Pure Appl. Math. XXX (1977), 543-571.

    [2] D. Burns, Curvature of the Monge-Amp`ere foliation and parabolic manifolds, Ann. of Math. 115 (1982), 349-373.

    [3] M. Kalka and G. Patrizio, Monge-Amp`ere Foliations for degenerate solutions, Ann. Mat. Pura Appl., 189 (2010), 381-393.

    [4] M. Kalka and G. Patrizio, Locally Monge-Amp`ere Parabolic Foliations, To appear in Adv. Geom.

    [5] G. Patrizio, A characterization of complex manifolds biholomorphic to a circular domain, Math. Z. 189 (1985), 343-363.

    [6] W. Stoll, The characterization of strictly parabolic manifolds, Ann. Scuola Norm. Sup. di Pisa, s. IV VII (1) (1980), 87-154.

    [7] Pit-Mann Wong On Umbilical Hypersurfaces and Uniformization of Circular Domains, In “Complex Analysis of several Variables”, Proc. Symp. Pure Math. 41, A.M.S., Providence, 1984. 225-252.

    Morris Kalka Mathematics Department Tulane University 6823 St. Charles Ave.

    New Orleans, LA 70118 USA E-mail: kalka@math.tulane.edu

  • Metrics
Share - Bookmark