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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

IMPACT FACTOR 2018: 0.789

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Mathematical Citation Quotient (MCQ) 2018: 0.53

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Volume 15, Issue 4


Locally Monge–Ampère parabolic foliations

Morris Kalka / Giorgio Patrizio
  • Corresponding author
  • Dip. Matematica e Informatica “U. Dini”, Università di Firenze, Viale Morgani 67/a 50134 Firenze, Italy
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Published Online: 2015-10-06 | DOI: https://doi.org/10.1515/advgeom-2015-0029


It is shown that codimension one parabolic foliations of complex manifolds are holomorphic. This is proved using the facts that codimension one foliations of complex manifolds are necessarily locally Monge- Ampère foliations and that parabolic leaves cannot have hyperbolic behavior. The result holds true also for locally Monge-Ampère foliations with parabolic leaves of arbitrary codimension.

Keywords: Monge-Ampère foliations; homogeneous complex Monge-Ampère equation; parabolic manifolds

About the article

Received: 2013-10-11

Published Online: 2015-10-06

Published in Print: 2015-10-01

Citation Information: Advances in Geometry, Volume 15, Issue 4, Pages 433–444, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2015-0029.

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