Subspaces of Multisymplectic Vector Spaces

TL;DR

This paper reviews existing orthogonality concepts in multisymplectic geometry, introduces a new orthogonality type, and analyzes subspaces of G_2-vector spaces using both notions.

Contribution

It proposes a novel orthogonality concept in multisymplectic geometry and explores its properties and implications for subspace structures.

Findings

New orthogonality concept developed and analyzed

Subspaces of G_2-vector spaces characterized using both orthogonality types

Several theoretical results proved about the properties of these subspaces

Abstract

A notion of orthogonality in multisymplectic geometry has been developed by Cantrijn, Ibort and de Le\'on and used by many authors. In this paper, we review this concept and propose a new type of orthogonality in multisymplectic geometry; we prove a number of results regarding this orthogonality and its associated subspaces. We end by calculating the various subspaces of a G_2-vector space based on both types of orthogonality.