Spray-Invariant Sets in Infinite-Dimensional Manifolds

[2505.10980] Spray-Invariant Sets in Infinite-Dimensional Manifolds Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Differential Geometry arXiv:2505.10980 (math) [Submitted on 16 May 2025 ( v1 ), last revised 10 Oct 2025 (this version, v2)] Title: Spray-Invariant Sets in Infinite-Dimensional Manifolds Authors: Kaveh Eftekharinasab View a PDF of the paper titled Spray-Invariant Sets in Infinite-Dimensional Manifolds, by Kaveh Eftekharinasab View PDF HTML (experimental) Abstract: We introduce the concept of spray-invariant sets on infinite-dimensional manifolds, where any geodesic of a spray starting in the set stays within it for its entire domain. These sets, possibly including singular spaces such as stratified spaces, exhibit different geometric properties depending on their regularity: sets that are not differentiable submanifolds may show sensitive dependence, for example, on parametrization, whereas for differentiable submanifolds invariance is preserved under reparametrization. This framework offers a broader perspective on geodesic preservation than the rigid notion of totally geodesic submanifolds, with examples arising naturally even in simple settings, such as linear spaces equipped with flat sprays. Subjects: Differential Geometry (math.DG) MSC classes: 58B20, 53C22, 37B35 Cite as: arXiv:2505.10980 [math.DG] (or arXiv:2505.10980v2 [math.DG] for this version) https://doi.org/10.48550/arXiv.2505.10980 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Bol. Soc. Paran. Mat., (3s.) v. , 2026 (44) : 1-26 Related DOI : https://doi.org/10.5269/bspm.77114 Focus to learn more DOI(s) linking to related resources Submission history From: Kaveh Eftekharinasab [ view email ] [v1] Fri, 16 May 2025 08:28:25 UTC (33 KB) [v2] Fri, 10 Oct 2025 12:44:50 UTC (35 KB) Full-text links: Access Paper: View a PDF of the paper titled Spray-Invariant Sets in Infinite-Dimensional Manifolds, by Kaveh Eftekharinasab View PDF HTML (experimental) TeX Source view license Current browse context: math.DG < prev | next > new | recent | 2025-05 Change to browse by: math 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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