Surfaces with mean of the hyperbolic curvature radii of double harmonic type

Authors

  • Armando M. V. Corro Instituto de Matemática e Estatística, Universidade Federal de Goias, Goiania-GO, Brazil.
  • Carlos M. C. Riveros Departamento de Matemática, Universidade de Brasília, Brasília, DF, Brazil.
  • Raquel P. de Aráujo Instituto Federal Goiano, Posee, GO, Brazil.

DOI:

https://doi.org/10.17268/sel.mat.2025.01.03

Keywords:

Hyperbolic curvature radii, holomorphic functions, Weingarten surfaces

Abstract

In this paper, we define surfaces with mean of the hyperbolic curvature radii of double harmonic type (in short DHRMC-surfaces) in the hyperbolic space, these surfaces include the generalized Weingarten surfaces of the harmonic type (HGW-surfaces). We give a characterization of DHRMCsurfaces.

Given a real function, we will present a family of DHRMC-surfaces that depend on two holomorphic functions. Moreover, we classify the DHRMC-surfaces of rotation.

References

Corro AV. Generalized Weingarten Surfaces of Bryant type in hyperbolic 3-space. XIV School on Differential Geometry (Portuguese). Mat. Contemp. 2006; 30:71–89.

Corro AMV, Fernandes KV, Riveros CMC. Generalized Weingarten Surfaces of harmonic type in hiperbolic 3-Space. Differential Geometry and its Applications. 2018; (58):202–226.

Corro AV, Pina R, Souza M. Surfaces of Rotation with Constant Extrinsic Curvature in a Conformally Flat 3-Space. Results. Math. 2011; 60:225–234.

Espinar JM, Gálvez JA, Mira P. Hypersurfaces in Hn+1 and conformally invariant equations: the generalized Christoffel and Nirenberg problems. J. Eur. Math. Soc. 2009; 11(4):903–939.

Machado CDF, Riveros CMC. Weingarten hypersurfaces of the spherical type in Euclidean spaces. Commentationes Mathematicae Universitatis Carolinae, vol. 2020; 61(2):213–236.

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Published

2025-07-26

How to Cite

V. Corro, A. M., C. Riveros, C. M., & P. de Aráujo, R. (2025). Surfaces with mean of the hyperbolic curvature radii of double harmonic type. Selecciones Matemáticas, 12(01), 33 - 43. https://doi.org/10.17268/sel.mat.2025.01.03

Issue

Vol. 12 No. 01 (2025): January - July

Section

Articles

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