Immersions in a Quaternionic Grassmannian inducing a given 4-form

2012/12/24 by Mahuya Datta, Datta, Mahuya
Mathematics · Physics and Astronomy · #53C07 #57R42 #58A10 #58B05 #58J99 #Advanced Differential Geometry Research #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1212.5885

openalex publication_date 2012/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Gr_k(\Hⁿ) be the Grassmannian manifold of Quaternionic k-planes in \Hⁿ and let γⁿ_k→ Gr_k(\Hⁿ) denote the Stiefel bundle of quaternionic k-frames in \Hⁿ. Let σ denote the first symplectic Pontrjagin form associated with the universal connection on γⁿ_k. We show that every 4-form ω on a smooth manifold M can be induced from σ by a smooth immersion f:M→ Gr_k(\Hⁿ) (for sufficiently large k and n) provided there exists a continuous map f₀:M→ Gr_k(\Hⁿ) which pulls back the cohomology class of σ onto that of ω.

Citations

• Existence of Universal Connections

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