Clifford structures, bilegendrian surfaces, and extrinsic curvature

Graham Smith

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arXiv · 2308.06919

Clifford structures, bilegendrian surfaces, and extrinsic curvature

Graham Smith

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Abstract

We use Clifford algebras to construct a unified formalism for studying constant extrinsic curvature immersed surfaces in riemannian and semi-riemannian $3$-manifolds in terms of immersed bilegendrian surfaces in their unitary bundles. As an application, we provide full classifications of both complete and compact immersed bilegendrian surfaces in the unit tangent bundle $\text{U}\Bbb{S}^3$ of the $3$-sphere.

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Graham Smith. 2023-08-14. Clifford structures, bilegendrian surfaces, and extrinsic curvature. https://arxiv.org/abs/2308.06919

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