Cubic curves and conics associated to the sphere S4
Abstract
This note introduces a \(1\)-parameter of cubic curves naturally associated to the sphere \(S^4\) considered in the unique \(5\)-dimensional irreducible representation space of \(SO(3)\). Eight examples are discussed with the last two being elliptic curves. Also, two conics are defined naturally in our setting by a special basis of the Lie algebra \(sl(3, \mathbb{R})\).
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Algebraic Geometry and Number Theory
Geometry and complex manifolds
Publication details
- Journal / source
- Open Journal of Mathematical Sciences
- Publisher
- Ptolemy Scientific Research Press
- Volume
- 10
- Pages
- 11–16
- Publication date
- 19 January 2026