Journal
JOURNAL OF GEOMETRY AND PHYSICS
Volume 195, Issue -, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.geomphys.2023.105055
Keywords
alpha-Catenary; Singular minimal surface; Ruled surface; Lorentz-Minkowski space
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In this paper, we study surfaces with minimal potential energy under gravitational forces, which are called singular minimal surfaces. We prove that a ruled singular minimal surface in a Euclidean 3-space is cylindrical, specifically an alpha-catenary cylinder, based on a result by Lopez. This result is also extended to Lorentz-Minkowski 3-space.
In this paper we study surfaces with minimal potential energy under gravitational forces, called singular minimal surfaces. We prove that a ruled singular minimal surface in a Euclidean 3-space is cylindrical, in particular as an alpha-catenary cylinder by a result of Lopez [Ann. Glob. Anal. Geom. 53 (4) (2018) 521-541]. This result is also extended in Lorentz-Minkowski 3-space.(c) 2023 Elsevier B.V. All rights reserved.
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