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Abstract.
In a contact manifold 
, we consider almost complex structures J that satisfy, for any vector v in the horizontal distribution, 
. We prove that two-dimensional integral cycles whose approximate tangent planes have the property of being J-invariant and positively oriented are in fact smooth Legendrian curves except possibly at isolated points and we investigate how such structures J are related to calibrations.
Keywords: Contact 5-manifold; Legendrian curve; almost complex structure; calibrations; minimal and almost-minimal surfaces; integral cycles
Received: 2011-04-20
Revised: 2012-07-12
Accepted: 2012-08-07
Published Online: 2013-07-01
Published in Print: 2013-07-01
© 2013 by Walter de Gruyter Berlin Boston
