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Annals of Global Analysis and Geometry最新文献

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Torsionless three-dimensional Heterotic solitons with harmonic curvature are rigid 具有谐波曲率的无扭转三维异质孤子是刚性的
IF 0.8 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2026-10-17 DOI: 10.1007/s10455-026-10065-0
Andrei Moroianu, Miguel Pino Carmona, C. S. Shahbazi
{"title":"Torsionless three-dimensional Heterotic solitons with harmonic curvature are rigid","authors":"Andrei Moroianu,&nbsp;Miguel Pino Carmona,&nbsp;C. S. Shahbazi","doi":"10.1007/s10455-026-10065-0","DOIUrl":"10.1007/s10455-026-10065-0","url":null,"abstract":"<div><p>We prove the following rigidity result: every compact three-dimensional Heterotic soliton with vanishing torsion and harmonic curvature is rigid, namely, it is an isolated point in the moduli space.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"70 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189821","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Solving the index problem for (curved) Bernstein–Gelfand–Gelfand sequences 求解（弯曲）Bernstein-Gelfand-Gelfand序列的指标问题
IF 0.8 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2026-10-14 DOI: 10.1007/s10455-026-10062-3
Magnus Goffeng
{"title":"Solving the index problem for (curved) Bernstein–Gelfand–Gelfand sequences","authors":"Magnus Goffeng","doi":"10.1007/s10455-026-10062-3","DOIUrl":"10.1007/s10455-026-10062-3","url":null,"abstract":"<div><p>We study the index theory of curved Bernstein–Gelfand–Gelfand (BGG) sequences in parabolic geometry and their role in <i>K</i>-homology and noncommutative geometry. The BGG-sequences fit into <i>K</i>-homology, and we solve their index problem. We provide a condition for when the BGG-complex on the flat parabolic geometry <i>G</i>/<i>P</i> of a semisimple Lie group <i>G</i> fits into <i>G</i>-equivariant <i>K</i>-homology by means of Heisenberg calculus. For higher rank Lie groups, we prove a no-go theorem showing that the approach fails.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"70 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-026-10062-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
J-Einstein critical metrics for quadratic curvature functionals 二次曲率泛函的j -爱因斯坦临界度量
IF 0.8 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2026-10-13 DOI: 10.1007/s10455-026-10064-1
Xiaomin Chen, Halyson Baltazar
{"title":"J-Einstein critical metrics for quadratic curvature functionals","authors":"Xiaomin Chen,&nbsp;Halyson Baltazar","doi":"10.1007/s10455-026-10064-1","DOIUrl":"10.1007/s10455-026-10064-1","url":null,"abstract":"<div><p>Lin-Yuan introduced the concept of the <i>J</i>-Einstein metric, which is a generalization of Bach-flat metric on 4-dimensional manifolds. In this article, we study the <i>J</i>-Einstein metrics as the critical point of quadratic curvature functionals involving the Ricci curvature and scalar curvature. We get some interesting results, which can be viewed as the improvement of Sheng-Wang’s conclusions on Bach-flat critical metrics (Bach-flat critical metrics for quadratic curvature functionals, <i>Ann. Glob. Anal. Geom.</i> 2018).</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"70 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Submanifolds of almost quaternionic skew-Hermitian manifolds 几乎四元数偏斜厄米流形的子流形
IF 0.8 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2026-10-12 DOI: 10.1007/s10455-026-10061-4
Ioannis Chrysikos, Jan Gregorovič
{"title":"Submanifolds of almost quaternionic skew-Hermitian manifolds","authors":"Ioannis Chrysikos,&nbsp;Jan Gregorovič","doi":"10.1007/s10455-026-10061-4","DOIUrl":"10.1007/s10455-026-10061-4","url":null,"abstract":"<div><p>We investigate several classes of submanifolds of almost quaternionic skew-Hermitian manifolds <span>((M^{4n}, Q, omega ))</span>, including almost symplectic, almost complex, almost pseudo-Hermitian and almost quaternionic submanifolds. In the torsion-free case, we realize each type of submanifold considered in the theoretical part by constructing explicit examples of submanifolds of semisimple quaternionic skew-Hermitian symmetric spaces.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"70 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Harmonic maps into nonnegatively curved manifolds and the soul theorem 调和映射到非负弯曲流形和灵魂定理
IF 0.8 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2026-10-07 DOI: 10.1007/s10455-026-10060-5
Sergey E. Stepanov, Josef Mikeš
{"title":"Harmonic maps into nonnegatively curved manifolds and the soul theorem","authors":"Sergey E. Stepanov,&nbsp;Josef Mikeš","doi":"10.1007/s10455-026-10060-5","DOIUrl":"10.1007/s10455-026-10060-5","url":null,"abstract":"<div><p>We study harmonic maps <i>f</i>: <span>((M,g)rightarrow (bar{M},bar{g}))</span> satisfying the curvature inequality <span>(textrm{Ric}_g ge f^{*}textrm{Ric}_{bar{g}})</span>. Using the Bochner identity, we show that if the sectional curvature of the target manifold is nonnegative along the image of the map, then every harmonic map from a compact manifold is totally geodesic, and it is constant whenever the inequality is strict at some point. Combining this result with Perelman’s proof of the Soul Conjecture, we obtain a rigidity theorem for harmonic maps into complete noncompact manifolds with nonnegative sectional curvature. In particular, if the image of the map contains a point at which all sectional curvatures of the target are strictly positive, then the soul of the tangent is a point. We also analyze the equality case of the Bochner identity and show that the images of eigendirections corresponding to eigenvalues of <span>(f^{bar{g}})</span> span two-planes of zero sectional curvature in the tanget manifold.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"70 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On a class of almost Hermitian 4-manifolds 一类几乎厄米4流形
IF 0.8 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2026-09-26 DOI: 10.1007/s10455-026-10059-y
Ethan Addison, Tedi Drăghici, Mehdi Lejmi
{"title":"On a class of almost Hermitian 4-manifolds","authors":"Ethan Addison,&nbsp;Tedi Drăghici,&nbsp;Mehdi Lejmi","doi":"10.1007/s10455-026-10059-y","DOIUrl":"10.1007/s10455-026-10059-y","url":null,"abstract":"<div><p>Using an integral identity of Sekigawa for compact almost Hermitian 4-manifolds, we naturally obtain a global characterization of the class <span>(mathcal{A}mathcal{H}_1)</span> of almost Hermitian 4-manifolds satisfying the first Gray curvature condition from apparently weaker conditions. Then we take steps towards a classification of almost Hermitian 4-manifolds of class <span>(mathcal{A}mathcal{H}_1)</span>, including proving a uniqueness result on 4-dimensional Lie algebras.\u0000</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"70 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132932","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On ( U(1)^{n-2} )-invariant special Lagrangian n-folds 关于( U(1)^{n-2} ) -不变的特殊拉格朗日n-褶
IF 0.8 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2026-09-18 DOI: 10.1007/s10455-026-10058-z
Mia S. L. Beard
{"title":"On ( U(1)^{n-2} )-invariant special Lagrangian n-folds","authors":"Mia S. L. Beard","doi":"10.1007/s10455-026-10058-z","DOIUrl":"10.1007/s10455-026-10058-z","url":null,"abstract":"<div><p>This paper develops a construction of families of <span>( U(1)^{n-2} )</span>-invariant special Lagrangian <i>n</i>-folds in <span>( mathbb {C}^{n} )</span>, extending the analytic framework introduced by Joyce (<span>( n = 3 )</span>) to arbitrary dimension. By reducing the special Lagrangian condition to a quasilinear elliptic system of two-dimensional non-linear Cauchy-Riemann equations, we analyse both the resulting geometry and its degenerations at singular points. We show that the structure and multiplicity of singularities are governed by an associated polynomial arising from the symmetry reduction. Explicit examples are constructed, including affine and perturbative solutions, and are compared with the classical Harvey-Lawson <span>( U(1)^{n-1} )</span>-invariant submanifolds. We further show that the key elements of Joyce’s analysis in the non-singular case, in particular the potential formulation and Dirichlet problem, extend to this higher-dimensional setting, with the proofs unchanged.\u0000</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"70 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-026-10058-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148986913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Klein bottle and optimal systolic inequality for nonpositively curved surfaces 非正曲面的克莱因瓶和最优收缩不等式
IF 0.8 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2026-09-08 DOI: 10.1007/s10455-026-10057-0
Mikhail G. Katz, Stéphane Sabourau
{"title":"Klein bottle and optimal systolic inequality for nonpositively curved surfaces","authors":"Mikhail G. Katz,&nbsp;Stéphane Sabourau","doi":"10.1007/s10455-026-10057-0","DOIUrl":"10.1007/s10455-026-10057-0","url":null,"abstract":"<div><p>We show that the systolic area of every nonpositively curved closed surface <i>M</i> other than the torus is at least 1, with equality if and only if <i>M</i> is isometric to a square flat Klein bottle. The proof focuses on the Klein-double <span>(4{mathbb {R}mathbb {P}}^2)</span> and exploits Weil’s isoperimetric inequality and a comparison theorem involving a new kind of exponential-type map.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"70 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-026-10057-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148903452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Courant algebroid lifts and curved Courant algebroids 柯朗代数提升和弯曲柯朗代数
IF 0.8 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2026-09-02 DOI: 10.1007/s10455-026-10050-7
Filip Moučka, Roberto Rubio
{"title":"Courant algebroid lifts and curved Courant algebroids","authors":"Filip Moučka,&nbsp;Roberto Rubio","doi":"10.1007/s10455-026-10050-7","DOIUrl":"10.1007/s10455-026-10050-7","url":null,"abstract":"<div><p>We introduce the Courant algebroid lift, a new construction that takes a Courant algebroid together with a vector bundle connection and produces, when the connection is flat in the image of the anchor, a Courant algebroid. In general, this lift produces a Courant-like structure that we call a curved Courant algebroid. We start by establishing a hierarchy of Courant algebroid properties and their associated structures. In this setting, we introduce curved Courant algebroids, which we show to be related to connections with torsion and curved differential graded Lie algebras. We use this to provide a classification of exact curved Courant algebroids. We show that the Courant algebroid lift of an exact Courant algebroid yields a natural link between the Patterson-Walker metric and generalized geometry. By lifting non-exact Courant algebroids, we establish a relation of these lifts to Lie algebras, Poisson and special complex geometry. Finally, we show that Courant algebroid lifts provide a large class of examples of Courant algebroid actions.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"70 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-026-10050-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148926569","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Vector-Valued Singular Integrals on Locally Doubling Spaces 局部倍空间上的向量值奇异积分
IF 0.8 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2026-08-10 DOI: 10.1007/s10455-026-10055-2
Mattia Calzi, Elena Rizzo
{"title":"Vector-Valued Singular Integrals on Locally Doubling Spaces","authors":"Mattia Calzi,&nbsp;Elena Rizzo","doi":"10.1007/s10455-026-10055-2","DOIUrl":"10.1007/s10455-026-10055-2","url":null,"abstract":"<div><p>We prove vector-valued boundedness of (suitable) Calderón-Zygmund operators and of the (truncated) Hardy–Littlewood maximal function on a <i>connected</i> locally doubling metric measure space.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"70 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751441","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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