Differential Geometry and its Applications最新文献

{"title":"Antipodal sets of pseudo-Riemannian symmetric R-spaces","authors":"Kyoji Sugimoto","doi":"10.1016/j.difgeo.2023.102104","DOIUrl":"https://doi.org/10.1016/j.difgeo.2023.102104","url":null,"abstract":"<div><p>We show that antipodal sets of pseudo-Riemannian symmetric <em>R</em>-spaces associated with non-degenerate Jordan triple systems satisfy the following two properties: (1) Any antipodal set is included in a great antipodal set, and (2) any two great antipodal sets are transformed into each other by an isometry.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139379283","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 prescribed fractional Q-curvatures problem on Sn under pinching conditions","authors":"Zhongwei Tang ,&nbsp;Ning Zhou","doi":"10.1016/j.difgeo.2023.102103","DOIUrl":"10.1016/j.difgeo.2023.102103","url":null,"abstract":"<div><p>In this paper, we study the prescribed fractional <em>Q</em>-curvatures problem of order 2<em>σ</em> on the <em>n</em>-dimensional standard sphere <span><math><mo>(</mo><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>,</mo><msub><mrow><mi>g</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></math></span>, where <span><math><mi>n</mi><mo>≥</mo><mn>3</mn></math></span>, <span><math><mi>σ</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mfrac><mrow><mi>n</mi><mo>−</mo><mn>2</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></math></span>. By combining critical points at infinity approach with Morse theory we obtain new existence results under suitable pinching conditions.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139092333","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":"When are shrinking gradient Ricci soliton compact","authors":"Yuanyuan Qu,&nbsp;Guoqiang Wu","doi":"10.1016/j.difgeo.2023.102102","DOIUrl":"10.1016/j.difgeo.2023.102102","url":null,"abstract":"<div><p>Suppose <span><math><mo>(</mo><msup><mrow><mi>M</mi></mrow><mrow><mn>4</mn></mrow></msup><mo>,</mo><mi>g</mi><mo>,</mo><mi>f</mi><mo>)</mo></math></span> is a complete shrinking gradient Ricci soliton. We give a sufficient condition for a soliton to be compact, generalizing previous result of Munteanu-Wang <span>[17]</span>. As an application, we give a classification of <span><math><mo>(</mo><msup><mrow><mi>M</mi></mrow><mrow><mn>4</mn></mrow></msup><mo>,</mo><mi>g</mi><mo>,</mo><mi>f</mi><mo>)</mo></math></span> under some natural conditions.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139078972","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":"Morse-Novikov cohomology on foliated manifolds","authors":"Md. Shariful Islam","doi":"10.1016/j.difgeo.2023.102100","DOIUrl":"https://doi.org/10.1016/j.difgeo.2023.102100","url":null,"abstract":"<div><p><span>The idea of Lichnerowicz or Morse-Novikov cohomology groups of a manifold has been utilized by many researchers to study important properties and invariants of a manifold. Morse-Novikov cohomology is defined using the differential </span><span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>ω</mi></mrow></msub><mo>=</mo><mi>d</mi><mo>+</mo><mi>ω</mi><mo>∧</mo></math></span>, where <em>ω</em><span><span> is a closed 1-form. We study Morse-Novikov cohomology relative to a foliation on a manifold and its homotopy invariance<span> and then extend it to more general type of forms on a Riemannian foliation. We study the Laplacian and Hodge decompositions for the corresponding </span></span>differential operators<span> on reduced leafwise Morse-Novikov complexes. In the case of Riemannian foliations, we prove that the reduced leafwise Morse-Novikov cohomology groups satisfy the Hodge theorem and Poincaré duality. The resulting isomorphisms yield a Hodge diamond structure for leafwise Morse-Novikov cohomology.</span></span></p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138839754","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":"The energy density of biharmonic quadratic maps between spheres","authors":"Rareş Ambrosie,&nbsp;Cezar Oniciuc","doi":"10.1016/j.difgeo.2023.102096","DOIUrl":"https://doi.org/10.1016/j.difgeo.2023.102096","url":null,"abstract":"<div><p><span>In this paper, we first prove that a quadratic form from </span><span><math><msup><mrow><mrow><mi>S</mi></mrow></mrow><mrow><mi>m</mi></mrow></msup></math></span> to <span><math><msup><mrow><mrow><mi>S</mi></mrow></mrow><mrow><mi>n</mi></mrow></msup></math></span> is non-harmonic biharmonic if and only if it has constant energy density <span><math><mo>(</mo><mi>m</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>/</mo><mn>2</mn></math></span>. Then, we give a positive answer to an open problem raised in <span>[1]</span> concerning the structure of non-harmonic biharmonic quadratic forms. As a direct application, using classification results for harmonic quadratic forms, we infer classification results for non-harmonic biharmonic quadratic forms.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138839752","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":"Bifurcations of robust features on surfaces in the Minkowski 3-space","authors":"Marco Antônio do Couto Fernandes","doi":"10.1016/j.difgeo.2023.102097","DOIUrl":"https://doi.org/10.1016/j.difgeo.2023.102097","url":null,"abstract":"<div><p><span>We obtain the bifurcation of some special curves on generic 1-parameter families of surfaces in the Minkowski 3-space. The curves treated here are the locus of points where the induced pseudo metric is degenerate, the discriminant of the lines </span>principal curvature<span>, the parabolic curve and the locus of points where the mean curvature vanishes.</span></p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138839753","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":"Vortex-type equations on compact Riemann surfaces","authors":"Kartick Ghosh","doi":"10.1016/j.difgeo.2023.102098","DOIUrl":"https://doi.org/10.1016/j.difgeo.2023.102098","url":null,"abstract":"<div><p>In this paper, we prove <em>a priori</em><span><span> estimates for some vortex-type equations on compact Riemann surfaces. As applications, we recover existing estimates for the vortex bundle Monge-Ampère equation, prove an </span>existence and uniqueness theorem for the Calabi-Yang-Mills equations on vortex bundles and get estimates for </span><em>J</em><span>-vortex equation. We prove an existence and uniqueness result relating Gieseker stability and the existence of almost Hermitian Einstein metrics, i.e., a Kobayashi-Hitchin type correspondence. We also prove Kählerness of the negative of the symplectic form which arises in the moment map interpretation of the Calabi-Yang-Mills equations in </span><span>[9]</span>.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138770022","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":"Existence and uniqueness results for a singular Kirchhoff type equation on a closed manifold","authors":"Mohamed El Farouk Ounane ,&nbsp;Kamel Tahri","doi":"10.1016/j.difgeo.2023.102094","DOIUrl":"10.1016/j.difgeo.2023.102094","url":null,"abstract":"<div><p><span><span><span>Using the variational methods and the </span>critical points theory, we prove the existence and the uniqueness of a positive solution for a singular </span>Kirchhoff<span> type equation on a closed Riemannian manifold of dimension </span></span><span><math><mi>N</mi><mo>≥</mo><mn>3</mn></math></span>. At the end, we give a geometric application involving the conformal Laplacian.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138683735","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":"Sphere bundle over the set of inner products in a Hilbert space","authors":"E. Andruchow ,&nbsp;M.E. Di Iorio y Lucero","doi":"10.1016/j.difgeo.2023.102092","DOIUrl":"10.1016/j.difgeo.2023.102092","url":null,"abstract":"<div><p>Let <span><math><mo>(</mo><mi>H</mi><mo>,</mo><mo>〈</mo><mspace></mspace><mo>,</mo><mspace></mspace><mo>〉</mo><mo>)</mo></math></span><span> be a complex Hilbert space and </span><span><math><mi>B</mi><mo>(</mo><mi>H</mi><mo>)</mo></math></span><span> the space of bounded linear operators in </span><span><math><mi>H</mi></math></span>. Any other equivalent inner product in <span><math><mi>H</mi></math></span> is of the form <span><math><msub><mrow><mo>〈</mo><mi>f</mi><mo>,</mo><mi>g</mi><mo>〉</mo></mrow><mrow><mi>A</mi></mrow></msub><mo>=</mo><mo>〈</mo><mi>A</mi><mi>f</mi><mo>,</mo><mi>g</mi><mo>〉</mo></math></span> (<span><math><mi>f</mi><mo>,</mo><mi>g</mi><mo>∈</mo><mi>H</mi></math></span>) for some positive invertible operator <span><math><mi>A</mi><mo>∈</mo><mi>B</mi><mo>(</mo><mi>H</mi><mo>)</mo></math></span>. In this paper we study the bundle <span><math><mi>M</mi></math></span> which consist of the unit sphere <span><math><mo>{</mo><mi>f</mi><mo>∈</mo><mi>H</mi><mo>:</mo><msub><mrow><mo>〈</mo><mi>f</mi><mo>,</mo><mi>f</mi><mo>〉</mo></mrow><mrow><mi>A</mi></mrow></msub><mo>=</mo><mn>1</mn><mo>}</mo></math></span> over each (equivalent) inner product <span><math><msub><mrow><mo>〈</mo><mspace></mspace><mo>,</mo><mspace></mspace><mo>〉</mo></mrow><mrow><mi>A</mi></mrow></msub></math></span>, which due to the observation above can be defined<span><span><span><math><mi>M</mi><mo>=</mo><mo>{</mo><mo>(</mo><mi>A</mi><mo>,</mo><mi>f</mi><mo>)</mo><mo>∈</mo><mi>B</mi><mo>(</mo><mi>H</mi><mo>)</mo><mo>×</mo><mi>H</mi><mo>:</mo><mi>A</mi><mtext> is positive and invertible and </mtext><mo>〈</mo><mi>A</mi><mi>f</mi><mo>,</mo><mi>f</mi><mo>〉</mo><mo>=</mo><mn>1</mn><mo>}</mo><mo>.</mo></math></span></span></span> We prove that <span><math><mi>M</mi></math></span><span><span> is a complemented submanifold of the </span>Banach space </span><span><math><mi>B</mi><mo>(</mo><mi>H</mi><mo>)</mo><mo>×</mo><mi>H</mi></math></span><span> and a homogeneous space of the Banach-Lie group </span><span><math><mi>G</mi><mo>(</mo><mi>H</mi><mo>)</mo><mo>⊂</mo><mi>B</mi><mo>(</mo><mi>H</mi><mo>)</mo></math></span> of invertible operators. We introduce a reductive structure in <span><math><mi>M</mi></math></span><span>, and study properties of the geodesics of the linear connection induced by this reductive structure. We consider certain submanifolds of </span><span><math><mi>M</mi></math></span>, for instance, the one obtained when the positive elements <em>A</em> describing the inner products lie in a prescribed C^⁎-algebra <span><math><mi>A</mi><mo>⊂</mo><mi>B</mi><mo>(</mo><mi>H</mi><mo>)</mo></math></span>.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138684010","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":"First eigenvalues of free boundary hypersurfaces in the unit ball along the inverse mean curvature flow","authors":"Pak Tung Ho ,&nbsp;Juncheol Pyo","doi":"10.1016/j.difgeo.2023.102095","DOIUrl":"https://doi.org/10.1016/j.difgeo.2023.102095","url":null,"abstract":"<div><p><span>In this note, we consider the first nonzero eigenvalue </span><span><math><msub><mrow><mi>λ</mi></mrow><mrow><mi>p</mi><mo>,</mo><mn>1</mn></mrow></msub></math></span> of the <em>p</em><span><span>-Laplacian on free boundary proper hypersurfaces in the unit ball evolving along the inverse </span>mean curvature flow. We show that </span><span><math><msub><mrow><mi>λ</mi></mrow><mrow><mi>p</mi><mo>,</mo><mn>1</mn></mrow></msub></math></span> is monotone decreasing along the flow. Using the convergence of free boundary disks in the unit ball, we give a lower bound of <span><math><msub><mrow><mi>λ</mi></mrow><mrow><mi>p</mi><mo>,</mo><mn>1</mn></mrow></msub></math></span> of a free boundary disk type hypersurface in the unit ball.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138582036","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}