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math.DG2026
Complex Quaternions and Superminimal Surfaces in Four-Space
Amedeo Altavilla, Elena Giorgio
We develop a quaternionic approach to conformal superminimal surfaces in Euclidean four-space. The starting point is the classical Weierstrass representation: every conformal minim…
math.DG2026
A Complete Characterization of Pythagorean Hodograph Preserving Mappings
Amedeo Altavilla, Hans-Peter Schröcker, ZbynÄk Å Ãr +1
We fully characterize the mappings that send every Pythagorean-hodograph (PH) curve to a PH curve. We prove that in any dimension, such mappings are precisely the conformal fu…
math.DG2026
The Flat CR Twistor Model and Its Algebraic Sections
Amedeo Altavilla, Stefano Marini
We study the flat CR twistor model by explicit projective methods. Using the anti-holomorphic involution associated with the twistor fibration, w…