Showing papers by "David E. Blair published in 2007"
TL;DR: In this article, the Lagrangian minimal submanifolds in {mathbb C}n were studied and it was shown that they are either flat and totally geodesic or they are homothetic to a piece of Lagrangians.
Abstract: Recently I. Castro and F. Urbano introduced the Lagrangian catenoid. Topologically, it is {mathbb R} \times Sn - 1 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 (n - 1)-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.
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