Search results
Search: MSC category 53C42
( Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42] )
1. CMB Online first
2. CMB 2015 (vol 59 pp. 50)
3. CMB 2010 (vol 53 pp. 516)
4. CMB 2008 (vol 51 pp. 448)
5. CMB 2007 (vol 50 pp. 321)
 Blair, David E.

On Lagrangian Catenoids
Recently I. Castro and F. Urbano introduced the
Lagrangian catenoid.
Topologically, it is $\mathbb R\times S^{n1}$ and its induced metric is
conformally flat,
but not cylindrical. Their result is that if a Lagrangian minimal
submanifold in
${\mathbb C}^n$ is foliated by round $(n1)$spheres, it is congruent to
a Lagrangian
catenoid. Here we study the question of conformally flat, minimal, Lagrangian
submanifolds in
${\mathbb C}^n$. The general problem is formidable, but we first show that such a
submanifold resembles a Lagrangian catenoid in that its Schouten tensor has an
eigenvalue of multiplicity one. Then, restricting to the case of at most two
eigenvalues, we show that the submanifold is either flat and totally
geodesic or is
homothetic to (a piece of) the Lagrangian catenoid.
Categories:53C42, 53D12 
