Voss Surfaces in Sine-Gordon Hierarchies

[2511.15558] Voss Surfaces in Sine-Gordon Hierarchies Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Differential Geometry arXiv:2511.15558 (math) [Submitted on 19 Nov 2025 ( v1 ), last revised 14 Aug 2026 (this version, v3)] Title: Voss Surfaces in Sine-Gordon Hierarchies Authors: Michal Marvan View a PDF of the paper titled Voss Surfaces in Sine-Gordon Hierarchies, by Michal Marvan View PDF HTML (experimental) Abstract: We explore a method, initiated by Guichard in 1890, which allows to generate sequences of Voss surfaces, starting from an arbitrarily chosen pseudospherical surface and a seed solution of the Moutard equation, by means of two simple transformations. In this paper, we 1) identify the Guichard transformations with the well-known recursion operator for symmetries of the sine-Gordon equation and its inverse; 2) prove a lemma which allows us to derive the length of Guichard's sequences from the invariance properties of the initial sine-Gordon solution; 3) introduce an extended class of inverted operators, expanding the class of Voss surfaces obtainable by quadratures; 4) clarify relevant aspects of Guthrie's formalism, paving the way for the future employment of the entire division algebra of recursion operators. A number of Voss nets are presented explicitly. Subjects: Differential Geometry (math.DG) ; Exactly Solvable and Integrable Systems (nlin.SI) MSC classes: 35A30, 37K10, 53A05, 58J70 Cite as: arXiv:2511.15558 [math.DG] (or arXiv:2511.15558v3 [math.DG] for this version) https://doi.org/10.48550/arXiv.2511.15558 Focus to learn more arXiv-issued DOI via DataCite Journal reference: SIGMA 22 (2026), 075, 26 pages Related DOI : https://doi.org/10.3842/SIGMA.2026.075 Focus to learn more DOI(s) linking to related resources Submission history From: Michal Marvan [ view email ] [via Journal Sigma as proxy] [v1] Wed, 19 Nov 2025 15:51:01 UTC (2,183 KB) [v2] Tue, 2 Jun 2026 12:23:39 UTC (2,188 KB) [v3] Fri, 14 Aug 2026 20:11:51 UTC (2,159 KB) Full-text links: Access Paper: View a PDF of the paper titled Voss Surfaces in Sine-Gordon Hierarchies, by Michal Marvan View PDF HTML (experimental) TeX Source view license Current browse context: math.DG < prev | next > new | recent | 2025-11 Change to browse by: math nlin nlin.SI References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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