Short Remark on (<i>p</i>₁,<i>p</i>₂,<i>p</i>₃)-Complex Numbers

Abstract

Movements on surfaces of centered Euclidean spheres and changes between those with different radii mean complex multiplication in R3. Here, the Euclidean norm, which generates the spheres, is replaced with an inhomogeneous functional and a product is introduced in a geometric analogy. Because a change in the radius now leads to a change in the shape of the sphere, a three-dimensional dynamic complex structure is created. Statements about invariant probability densities, generalized uniform distributions on generalized spheres, geometric measure representations, and dynamic ball numbers associated with this structure are also presented.

Keywords

• vector-valued product
• vector exponential function
• (<i>p</i>₁,<i>p</i>₂,<i>p</i>₃)-complex algebraic structure
• dynamic complex structure
• Euler type formula
• (<i>p</i>₁,<i>p</i>₂,<i>p</i>₃)-spherical coordinates