Differential geometry of grassmannians and Plucker map

TL;DR

This paper explores the geometry of grassmannians via the Plucker map, demonstrating that in hyperbolic cases, the Plucker map is a minimal isometric embedding, extending known results from elliptic cases.

Contribution

It extends the understanding of grassmannian geometries by analyzing the Plucker map in hyperbolic cases, showing it is a minimal isometric embedding.

Findings

Plucker map is a minimal isometric embedding in hyperbolic grassmannian geometries

Extends known results from elliptic to hyperbolic grassmannian cases

Provides foundational insights into grassmannian geometries using Plucker map

Abstract

Using the Plucker map between grassmannians, we study basic aspects of classic grassmannian geometries. For `hyperbolic' grassmannian geometries, we prove some facts (for instance, that the Plucker map is a minimal isometric embedding) that were previously known in the `elliptic' case.