Tori Embedded in R3 with Dense Principal Lines
Ronaldo Garcia, Jorge Sotomayor
TL;DR
This paper presents examples of tori embedded in three-dimensional space with all principal lines dense, achieved through stereographic projection of deformed Clifford tori in four-dimensional space.
Contribution
It introduces new embeddings of tori with dense principal lines using stereographic projection of deformed Clifford tori.
Findings
Examples of tori with all principal lines dense in R3.
Construction method via stereographic projection of deformed Clifford tori.
Insights into the geometry of dense principal lines on embedded tori.
Abstract
In this paper are given examples of tori T2 embedded in R3 with all their principal lines dense. These examples are obtained by stereographic projection of deformations of the Clifford torus in S3.
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Taxonomy
TopicsGeometric and Algebraic Topology · Microtubule and mitosis dynamics · Algebraic and Geometric Analysis