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 \({\text {U}}\mathbb {S}^3\) of the 3-sphere.

中文翻译：

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Clifford 结构、双传说曲面和外在曲率

我们使用 Clifford 代数构建了一个统一的形式体系，用于研究黎曼和半黎曼 3-流形中的恒定外在曲率浸入曲面，即酉丛中的浸入双勒本曲面。作为一个应用，我们提供了 3 球体的单位切丛\({\text {U}}\mathbb {S}^3\)中完整和紧凑浸没双勒根曲面的完整分类。