Willmore-Like Tori in Killing Submersions. (12th June 2018)

• Record Type: Journal Article
• Authors: Barros, Manuel; Garay, Óscar J.; Pámpano, Álvaro
• Other Names: Léandre Remi Academic Editor.
• Is Part Of: Advances in mathematical physics. Volume 2018(2018)
• Publication Date: 2018-06-12
• Subjects: Mathematical physics -- Periodicals; Mathematical physics; Periodicals; 530.15
• DOI: 10.1155/2018/4652516
• Languages: English
• ISSNs: 1687-9120

Abstract

Abstract : The first variation formula and Euler-Lagrange equations for Willmore-like surfaces in Riemannian 3-spaces with potential are computed and, then, applied to the study of invariant Willmore-like tori with invariant potential in the total space of a Killing submersion. A connection with generalized elastica in the base surface of the Killing submersion is found, which is exploited to analyze Willmore tori in Killing submersions and to construct foliations of Killing submersions made up of Willmore tori with constant mean curvature.