Gauss maps of surfaces in 3-dimensional Heisenberg group
Christiam Figueroa
TL;DR
This paper investigates the Gauss map of surfaces in the 3D Heisenberg group, linking its tension field to the surface's mean curvature using the Gans model of the hyperbolic plane.
Contribution
It establishes a novel relationship between the tension field of the Gauss map and the mean curvature for surfaces in the Heisenberg group.
Findings
Relationship between Gauss map tension field and mean curvature.
Use of Gans model to analyze hyperbolic plane geometry.
New insights into surface geometry in Heisenberg group.
Abstract
In this paper, we study the Gauss map of surfaces in 3-dimensional Heisenberg group using the Gans model of the hyperbolic plane. We establish a relationship between the tension field of the Gauss map and mean curvature of a surface in .
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometric and Algebraic Topology · Geometry and complex manifolds