This paper defines DHRMC-surfaces and classifies them using holomorphic functions, suggesting new insights into hyperbolic curvature.
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.
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Corro et al. (2025) studied this question.
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