Glasgow Mathematical Journal最新文献

{"title":"A Helfrich functional for compact surfaces in","authors":"Zhongwei Yao","doi":"10.1017/s0017089523000320","DOIUrl":"https://doi.org/10.1017/s0017089523000320","url":null,"abstract":"<p>Let <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231003124134699-0703:S0017089523000320:S0017089523000320_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$f;:; Mrightarrow mathbb{C}P^{2}$</span></span></img></span></span> be an isometric immersion of a compact surface in the complex projective plane <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231003124134699-0703:S0017089523000320:S0017089523000320_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$mathbb{C}P^{2}$</span></span></img></span></span>. In this paper, we consider the Helfrich-type functional <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231003124134699-0703:S0017089523000320:S0017089523000320_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$mathcal{H}_{lambda _{1},lambda _{2}}(f)=int _{M}(|H|^{2}+lambda _{1}+lambda _{2} C^{2})textrm{d} M$</span></span></img></span></span>, where <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231003124134699-0703:S0017089523000320:S0017089523000320_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$lambda _{1}, lambda _{2}in mathbb{R}$</span></span></img></span></span> with <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231003124134699-0703:S0017089523000320:S0017089523000320_inline6.png\"><span data-mathjax-type=\"texmath\"><span>$lambda _{1}geqslant 0$</span></span></img></span></span>, <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231003124134699-0703:S0017089523000320:S0017089523000320_inline7.png\"><span data-mathjax-type=\"texmath\"><span>$H$</span></span></img></span></span> and <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231003124134699-0703:S0017089523000320:S0017089523000320_inline8.png\"><span data-mathjax-type=\"texmath\"><span>$C$</span></span></img></span></span> are respectively the mean curvature vector and the Kähler function of <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231003124134699-0703:S0017089523000320:S0017089523000320_inline9.png\"><span data-mathjax-type=\"texmath\"><span>$M$</span></span></img></span></span> in <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231003124134699-0703:S0017089523000320:S0017089523000320_inline10.png\"><span data-mathjax-type=\"texmath\"><span>$mathbb{C}P^{2}$</span></span></img></span></span>. The critic","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":"88 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532318","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Null hypersurfaces in 4-manifolds endowed with a product structure","authors":"Nikos Georgiou","doi":"10.1017/s0017089523000319","DOIUrl":"https://doi.org/10.1017/s0017089523000319","url":null,"abstract":"Abstract In a 4-manifold, the composition of a Riemannian Einstein metric with an almost paracomplex structure that is isometric and parallel defines a neutral metric that is conformally flat and scalar flat. In this paper, we study hypersurfaces that are null with respect to this neutral metric, and in particular we study their geometric properties with respect to the Einstein metric. Firstly, we show that all totally geodesic null hypersurfaces are scalar flat and their existence implies that the Einstein metric in the ambient manifold must be Ricci-flat. Then, we find a necessary condition for the existence of null hypersurface with equal nontrivial principal curvatures, and finally, we give a necessary condition on the ambient scalar curvature, for the existence of null (non-minimal) hypersurfaces that are of constant mean curvature.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":"129 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135343983","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quantum symmetries of Cayley graphs of abelian groups","authors":"Daniel Gromada","doi":"10.1017/s0017089523000198","DOIUrl":"https://doi.org/10.1017/s0017089523000198","url":null,"abstract":"Abstract We study Cayley graphs of abelian groups from the perspective of quantum symmetries. We develop a general strategy for determining the quantum automorphism groups of such graphs. Applying this procedure, we find the quantum symmetries of the halved cube graph, the folded cube graph, and the Hamming graphs.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135637919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"GMJ volume 65 issue 3 Cover and Front matter","authors":"","doi":"10.1017/s0017089523000307","DOIUrl":"https://doi.org/10.1017/s0017089523000307","url":null,"abstract":"An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135687491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"GMJ volume 65 issue 3 Cover and Back matter","authors":"","doi":"10.1017/s0017089523000290","DOIUrl":"https://doi.org/10.1017/s0017089523000290","url":null,"abstract":"An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135687492","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Relative Dehn functions, hyperbolically embedded subgroups and combination theorems","authors":"H. Bigdely, Eduardo Martínez-Pedroza","doi":"10.1017/s0017089523000265","DOIUrl":"https://doi.org/10.1017/s0017089523000265","url":null,"abstract":"\u0000\t <jats:p>Consider the following classes of pairs consisting of a group and a finite collection of subgroups:<jats:list list-type=\"bullet\">\u0000\t <jats:list-item>\u0000\t\t<jats:label>•</jats:label>\u0000\t\t<jats:p>\u0000\t\t <jats:inline-formula>\u0000\t\t <jats:alternatives>\u0000\t\t <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089523000265_inline1.png\" />\u0000\t\t <jats:tex-math>\u0000$ mathcal{C}= left { (G,mathcal{H}) mid text{$mathcal{H}$ is hyperbolically embedded in $G$} right }$\u0000</jats:tex-math>\u0000\t\t </jats:alternatives>\u0000\t\t </jats:inline-formula>\u0000\t\t</jats:p>\u0000\t </jats:list-item>\u0000\t <jats:list-item>\u0000\t\t<jats:label>•</jats:label>\u0000\t\t<jats:p>\u0000\t\t <jats:inline-formula>\u0000\t\t <jats:alternatives>\u0000\t\t <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089523000265_inline2.png\" />\u0000\t\t <jats:tex-math>\u0000$ mathcal{D}= left { (G,mathcal{H}) mid text{the relative Dehn function of $(G,mathcal{H})$ is well-defined} right } .$\u0000</jats:tex-math>\u0000\t\t </jats:alternatives>\u0000\t\t </jats:inline-formula>\u0000\t\t</jats:p>\u0000\t </jats:list-item>\u0000\t </jats:list></jats:p>\u0000\t <jats:p>Let <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089523000265_inline3.png\" />\u0000\t\t<jats:tex-math>\u0000$G$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> be a group that splits as a finite graph of groups such that each vertex group <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089523000265_inline4.png\" />\u0000\t\t<jats:tex-math>\u0000$G_v$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> is assigned a finite collection of subgroups <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089523000265_inline5.png\" />\u0000\t\t<jats:tex-math>\u0000$mathcal{H}_v$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula>, and each edge group <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089523000265_inline6.png\" />\u0000\t\t<jats:tex-math>\u0000$G_e$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> is conjugate to a subgroup of some <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089523000265_inline7.png\" />\u0000\t\t<jats:tex-math>\u0000$Hin mathcal{H}_v$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> if <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089523000265_inline8.png\" />\u0000\t\t<jats:tex-math>\u0000$e$\u0000</jats:tex-math>\u0000\t </jats:alt","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47620609","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the structure of lower bounded HNN extensions","authors":"Paul Bennett, T. Jajcayová","doi":"10.1017/S001708952300023X","DOIUrl":"https://doi.org/10.1017/S001708952300023X","url":null,"abstract":"Abstract This paper studies the structure and preservational properties of lower bounded HNN extensions of inverse semigroups, as introduced by Jajcayová. We show that if \u0000$S^* = [ S;; U_1,U_2;; phi ]$\u0000 is a lower bounded HNN extension then the maximal subgroups of \u0000$S^*$\u0000 may be described using Bass-Serre theory, as the fundamental groups of certain graphs of groups defined from the \u0000$mathcal{D}$\u0000 -classes of \u0000$S$\u0000 , \u0000$U_1$\u0000 and \u0000$U_2$\u0000 . We then obtain a number of results concerning when inverse semigroup properties are preserved under the HNN extension construction. The properties considered are completely semisimpleness, having finite \u0000$mathcal{R}$\u0000 -classes, residual finiteness, being \u0000$E$\u0000 -unitary, and \u0000$0$\u0000 - \u0000$E$\u0000 -unitary. Examples are given, such as an HNN extension of a polycylic inverse monoid.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":"65 1","pages":"697 - 715"},"PeriodicalIF":0.5,"publicationDate":"2023-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46064272","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Geometric aspects on Humbert-Edge curves of type 5, Kummer surfaces and hyperelliptic curves of genus 2","authors":"Abel Castorena, Juan Bosco Fr'ias-Medina","doi":"10.1017/S0017089523000174","DOIUrl":"https://doi.org/10.1017/S0017089523000174","url":null,"abstract":"Abstract In this work, we study the Humbert-Edge curves of type 5, defined as a complete intersection of four diagonal quadrics in \u0000${mathbb{P}}^5$\u0000 . We characterize them using Kummer surfaces, and using the geometry of these surfaces, we construct some vanishing thetanulls on such curves. In addition, we describe an argument to give an isomorphism between the moduli space of Humbert-Edge curves of type 5 and the moduli space of hyperelliptic curves of genus 2, and we show how this argument can be generalized to state an isomorphism between the moduli space of hyperelliptic curves of genus \u0000$g=frac{n-1}{2}$\u0000 and the moduli space of Humbert-Edge curves of type \u0000$ngeq 5$\u0000 where \u0000$n$\u0000 is an odd number.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":"65 1","pages":"612 - 624"},"PeriodicalIF":0.5,"publicationDate":"2023-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48671226","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A presentation for the Eisenstein-Picard modular group in three complex dimensions","authors":"Jieyan Wang, Baohua Xie","doi":"10.1017/S0017089523000186","DOIUrl":"https://doi.org/10.1017/S0017089523000186","url":null,"abstract":"Abstract A. Mark and J. Paupert [Presentations for cusped arithmetic hyperbolic lattices, 2018, arXiv:1709.06691.] presented a method to compute a presentation for any cusped complex hyperbolic lattice. In this note, we will use their method to give a presentation for the Eisenstein-Picard modular group in three complex dimensions.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":"65 1","pages":"625 - 654"},"PeriodicalIF":0.5,"publicationDate":"2023-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42063740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"GMJ volume 65 issue S1 Cover and Front matter","authors":"","doi":"10.1017/s0017089523000095","DOIUrl":"https://doi.org/10.1017/s0017089523000095","url":null,"abstract":"","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":"65 1","pages":"f1 - f2"},"PeriodicalIF":0.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42888039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}