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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

CiteScore 2018: 0.73

SCImago Journal Rank (SJR) 2018: 0.329
Source Normalized Impact per Paper (SNIP) 2018: 0.908

Mathematical Citation Quotient (MCQ) 2018: 0.53

Online
ISSN
1615-7168
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Volume 15, Issue 4

Issues

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

Abstract

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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