Distance-squared mappings
Shunsuke Ichiki, Takashi Nishimura
TL;DR
This paper introduces extended distance-squared mappings in differential topology, exploring their properties and significance in singularity theory and differential geometry.
Contribution
It defines naturally extended distance-squared mappings and investigates their properties from a differential topology perspective, advancing understanding in singularity theory.
Findings
Extended mappings generalize classical distance-squared functions.
Properties of these mappings are characterized in the context of differential topology.
Potential applications in singularity theory and differential geometry are discussed.
Abstract
A distance-squared function is one of the most significant functions in the application of singularity theory to differential geometry. In this paper, we define naturally extended mappings of distance-squared functions, wherein each component is a distance-squared function. We investigate the properties of these mappings from the viewpoint of differential topology.
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Taxonomy
TopicsPolynomial and algebraic computation · Advanced Numerical Analysis Techniques · Algebraic and Geometric Analysis