Clifford结构，双列曲面和外在曲率

IF 0.5 4区数学 Q3 MATHEMATICS

Geometriae Dedicata Pub Date : 2023-11-27 DOI:10.1007/s10711-023-00855-2

Graham Smith

引用次数: 0

摘要

利用Clifford代数构造了一个统一的形式，用于研究黎曼和半黎曼3-流形中恒定外曲率浸没曲面在黎曼和半黎曼3-流形中的浸没曲面在黎曼和半黎曼3-流形中的正束浸没曲面。作为一种应用，我们在3球的单位切线束\({\text {U}}\mathbb {S}^3\)上给出了完全和紧致浸没双线曲面的完全分类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Clifford structures, bilegendrian surfaces, and extrinsic curvature

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.

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来源期刊

Geometriae Dedicata 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Geometriae Dedicata concentrates on geometry and its relationship to topology, group theory and the theory of dynamical systems. Geometriae Dedicata aims to be a vehicle for excellent publications in geometry and related areas. Features of the journal will include: A fast turn-around time for articles. Special issues centered on specific topics. All submitted papers should include some explanation of the context of the main results. Geometriae Dedicata was founded in 1972 on the initiative of Hans Freudenthal in Utrecht, the Netherlands, who viewed geometry as a method rather than as a field. The present Board of Editors tries to continue in this spirit. The steady growth of the journal since its foundation is witness to the validity of the founder''s vision and to the success of the Editors'' mission.