A \Gamma-structure on Lagrangian Grassmannians

TL;DR

This paper demonstrates that for odd n, the Lagrangian Grassmannian of a0a0^{2n} possesses a a0a0-structure, revealing new geometric properties of these manifolds.

Contribution

It establishes a a0a0-structure on Lagrangian Grassmannians for odd n, contributing to the understanding of their geometric and topological properties.

Findings

Lagrangian Grassmannian of a0a0^{2n} is a a0a0-manifold for odd n.

The a0a0-structure exists specifically when n is odd.

This structure provides new insights into the geometry of Lagrangian Grassmannians.

Abstract

For n odd the Lagrangian Grassmannian of \R^{2n} is a \Gamma-manifold.