Surfaces with quadratic support function of harmonic type
Armando M.V. Corro, Carlos M.C. Riveros, Jos\'e L. Teruel
TL;DR
This paper introduces a new class of surfaces in three-dimensional space called HQSF-surfaces, generalizing QSF-surfaces, and provides a Weierstrass representation and classification for rotational cases.
Contribution
It develops a Weierstrass type representation for HQSF-surfaces based on three holomorphic functions and classifies rotational HQSF-surfaces.
Findings
Derived a Weierstrass type representation for HQSF-surfaces.
Classified HQSF-surfaces of rotation.
Generalized QSF-surfaces to a broader class.
Abstract
In this paper, we study oriented surfaces S in , called Surfaces with quadratic support function of harmonic type (in short HQSF-surfaces), these surfaces generalize the QSF-surfaces. We obtain a Weierstrass type representation for the HQSF-surfaces which depends on three holomorphic functions. Moreover, we classify the HQSF-surfaces of rotation.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Holomorphic and Operator Theory · Analytic and geometric function theory