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Rotational Weingarten surfaces in hyperbolic 3-space

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We study rotational Weingarten surfaces in the hyperbolic space \(\mathbb {H}^3(-1)\) with the principal curvatures \(\kappa \) and \(\lambda \) satisfying a certain functional relation \(\kappa = F(\lambda )\) for a given continuous function F. We determine profile curves of such surfaces parameterized in terms of the principal curvature \(\lambda \). Then we consider some special cases by taking \(F(\lambda ) = a\lambda + b\) and \(F(\lambda ) = a\lambda ^m\) for particular values of the constants a, b, and m.

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Acknowledgements

We would like to thank the referee for carefully reading the manuscript and giving constructive comments, which help to improve the quality of this manuscript.

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  1. Department of Mathematics, Faculty of Arts and Sciences, Işık University, Şile Campus, 34980, Şile, Istanbul, Turkey

    Uğur Dursun

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  1. Uğur Dursun
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Dursun, U. Rotational Weingarten surfaces in hyperbolic 3-space. J. Geom. 111, 7 (2020). https://doi.org/10.1007/s00022-019-0519-6

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  • DOI: https://doi.org/10.1007/s00022-019-0519-6

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