A topological constraint for monotone Lagrangians in hypersurfaces of Kähler manifolds

Abstract

In this paper is established a topological constraint for monotone Lagrangian embeddings in certain complex hypersurfaces of integral Kähler manifolds. As an application, we prove that it is impossible to embed a connected sum of $S^1\times S^{2k}$s in $\mathbb{C}{P}^{2k+1}$ as a monotone Lagrangian.

15 pages