A note on precotangent bundles: the example of Grassmannians

TL;DR

This paper establishes the existence of a predual bundle, called the precotangent bundle, for Grassmannians of reflexive Banach spaces and p-restricted Grassmannians of polarized Hilbert spaces, expanding geometric understanding.

Contribution

It introduces the concept of the precotangent bundle and proves its existence in specific infinite-dimensional Grassmannian settings, a novel extension in geometric analysis.

Findings

Existence of the precotangent bundle for Grassmannians of reflexive Banach spaces.

Existence of the precotangent bundle for p-restricted Grassmannians of polarized Hilbert spaces.

Provides foundational results for further geometric and analytical studies in infinite-dimensional settings.

Abstract

We prove the existence of the bundle predual to the tangent bundle (called precotangent bundle) for Grassmannians of reflexive Banach spaces and $p$-restricted Grassmannians of the polarized Hilbert space.