Graph-type biharmonic surfaces in R3
DOI:
https://doi.org/10.17268/sel.mat.2020.01.08Keywords:
Biharmonic surfaces, Harmonic surfaces, Gaussian curvatureAbstract
In this work, we study biharmonic surfaces that are parameterized by biharmonic coordinate functions. We study a class of biharmonic surfaces called graph-type biharmonic surfaces. Also, we define a class of surfaces associated to two harmonic functions (FH2A-surfaces), these surfaces satisfy a relation between the Gaussian curvature, the projection of the Gauss map on a fixed plane and two harmonic functions. We show that a particular class of graph-type biharmonic surfaces are FH2A-surfaces. Finally, we classify the FH2A-surfaces of rotation.
References
Klotz T. Surfaces Harmonically Immersed in E3. Pacific Journal of Mathematics. 1967; 21(1): 79-87.
Riveros C, Corro A, Barbosa S. Superficies armónicas de tipo gráfico. Selecciones Matemáticas. 2016; 03(01):1-7.
Riveros C, Corro A. Laguerre Type Surfaces. Nexus Mathematicae. 2019; 1:16-29.
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