Math @ Duke

Publications [#10364] of Robert Bryant
search www.ams.org.Papers Published
 Leviflat minimal hypersurfaces in twodimensional complex space forms,
in Lie groups, geometric structures and differential equationsone hundred years after Sophus Lie (Kyoto/Nara, 1999), Adv. Stud. Pure Math., vol. 37
(2002),
pp. 144, Math. Soc. Japan [MR1980895], [math.DG/9909159]
(last updated on 2010/11/19)
Abstract: The purpose of this article is to classify the real
hypersurfaces in complex space forms of dimension 2
that are
both Leviflat and minimal. The main results are as
follows:
When the curvature of the complex space form is
nonzero, there is a 1parameter family of such
hypersurfaces.
Specifically, for each oneparameter subgroup of the
isometry
group of the complex space form, there is an
essentially
unique example that is invariant under this
oneparameter
subgroup.
On the other hand, when the curvature of the space
form is zero, i.e., when the space form is complex
2space
with its standard flat metric, there is an additional
`exceptional' example that has no continuous
symmetries but
is invariant under a lattice of translations. Up to
isometry
and homothety, this is the unique example with no
continuous
symmetries.


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