A topological constraint for monotone Lagrangians in hypersurfaces of K\"ahler manifolds

Abstract

In this paper is established a topological constraint for monotone Lagrangian embeddings in certain complex hypersurfaces of integral K\"ahler 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.