Cho, J., Hara, M., Polly, D., & Tada, T. (2025). Lie minimal Weingarten surfaces. HIROSHIMA MATHEMATICAL JOURNAL, 55(2), 151–165. https://doi.org/10.32917/h2023019
E104-03 - Forschungsbereich Differentialgeometrie und geometrische Strukturen
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Journal:
HIROSHIMA MATHEMATICAL JOURNAL
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ISSN:
0018-2079
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Date (published):
Jul-2025
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Number of Pages:
15
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Publisher:
HIROSHIMA UNIV, GRAD SCH SCI
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Peer reviewed:
Yes
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Keywords:
constant mean curvature surface; Lie minimal surface; linear Weingarten surface; minimal surface
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Abstract:
We consider Lie minimal surfaces, the critical points of the simplest Lie sphere invariant energy, in Riemannian space forms. These surfaces can be characterized via their Euler-Lagrange equations, which take the form of differential equations in terms of the principal curvatures. Surfaces with constant mean curvature that satisfy these equations turn out to be rotational in their space form. We generalize in flat ambient space: here surfaces whose principal curvatures satisfy an affine relationship as well as elliptic linear Weingarten surfaces are rotational as well.
