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arXiv · 2607.19016

Strictly paired ${\rm CR}$ linear automorphisms of $\R^4$

Ioannis D. Platis
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Abstract

This paper investigates the algebraic and differential geometric properties of smooth mappings between domains in $\mathbb{C}^2$, classifying them according to the constant ranks of their holomorphic and antiholomorphic derivative components. Particular emphasis is placed on strictly paired CR (SPCR) linear automorphisms of $\mathbb{R}^4$, where both block matrices $A$ and $B$ have rank 1. We characterise the set of SPCR linear automorphisms as a 12-dimensional submanifold of $\mathrm{GL}(2,\mathbb{C})^2$ and analyse its underlying CR structure, demonstrating its geometric and structural rigidity.

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Ioannis D. Platis. 2026-07-21. Strictly paired ${\rm CR}$ linear automorphisms of $\R^4$. https://arxiv.org/abs/2607.19016

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