Lagrangian submanifolds in k-symplectic settings

TL;DR

This paper generalizes Weinstein's normal form theorem for Lagrangian submanifolds from symplectic to k-symplectic manifolds, broadening the understanding of geometric structures in higher-dimensional settings.

Contribution

It extends the classical normal form theorem for Lagrangian submanifolds to the context of k-symplectic geometry, providing new theoretical insights.

Findings

Generalization of Weinstein's theorem to k-symplectic manifolds

Establishment of normal form results in higher-dimensional symplectic settings

Enhanced understanding of Lagrangian submanifolds in k-symplectic geometry

Abstract

In this paper we extend the well-know normal form theorem for Lagrangian submanifolds proved by A. Weinstein in symplectic geometry to the setting of k-symplectic manifolds.