发布求助
文献互助 智能选刊 最新文献

Journal of Differential Geometry最新文献

筛选
英文 中文
Blowups and blowdowns of geodesics in Carnot groups 卡诺群中测地线的爆破和爆破
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2018-06-25 DOI: 10.4310/jdg/1680883578
Eero Hakavuori, E. Donne
{"title":"Blowups and blowdowns of geodesics in Carnot groups","authors":"Eero Hakavuori, E. Donne","doi":"10.4310/jdg/1680883578","DOIUrl":"https://doi.org/10.4310/jdg/1680883578","url":null,"abstract":"This paper provides some partial regularity results for geodesics (i.e., isometric images of intervals) in arbitrary sub-Riemannian and sub-Finsler manifolds. Our strategy is to study infinitesimal and asymptotic properties of geodesics in Carnot groups equipped with arbitrary sub-Finsler metrics. We show that tangents of Carnot geodesics are geodesics in some groups of lower nilpotency step. Namely, every blowup curve of every geodesic in every Carnot group is still a geodesic in the group modulo its last layer. Then as a consequence we get that in every sub-Riemannian manifold any $s$ times iterated tangent of any geodesic is a line, where $s$ is the step of the sub-Riemannian manifold in question. With a similar approach, we also show that blowdown curves of geodesics in sub-Riemannian Carnot groups are contained in subgroups of lower rank. This latter result is also extended to rough geodesics.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2018-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43756235","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 16
Weakly symmetric pseudo–Riemannian nilmanifolds 弱对称伪黎曼零流形
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2018-06-21 DOI: 10.4310/jdg/1664378619
J. Wolf, Zhiqi Chen
{"title":"Weakly symmetric pseudo–Riemannian nilmanifolds","authors":"J. Wolf, Zhiqi Chen","doi":"10.4310/jdg/1664378619","DOIUrl":"https://doi.org/10.4310/jdg/1664378619","url":null,"abstract":"In an earlier paper we developed the classification of weakly symmetric pseudo--riemannian manifolds $G/H$ where $G$ is a semisimple Lie group and $H$ is a reductive subgroup. We derived the classification from the cases where $G$ is compact. As a consequence we obtained the classification of semisimple weakly symmetric manifolds of Lorentz signature $(n-1,1)$ and trans--lorentzian signature $(n-2,2)$. Here we work out the classification of weakly symmetric pseudo--riemannian nilmanifolds $G/H$ from the classification for the case $G = Nrtimes H$ with $H$ compact and $N$ nilpotent. It turns out that there is a plethora of new examples that merit further study. Starting with that riemannian case, we see just when a given involutive automorphism of $H$ extends to an involutive automorphism of $G$, and we show that any two such extensions result in isometric pseudo--riemannian nilmanifolds. The results are tabulated in the last two sections of the paper.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2018-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43135438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 6
Poles of cubic differentials and ends of convex $mathbb{RP}^2$-surfaces 三次微分的极点和凸$mathbb｛RP｝^2$曲面的端点
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2018-06-17 DOI: 10.4310/jdg/1679503805
Xin Nie
{"title":"Poles of cubic differentials and ends of convex $mathbb{RP}^2$-surfaces","authors":"Xin Nie","doi":"10.4310/jdg/1679503805","DOIUrl":"https://doi.org/10.4310/jdg/1679503805","url":null,"abstract":"On any oriented surface, the affine sphere construction gives a one-to-one correspondence between convex $mathbb{RP}^2$-structures and holomorphic cubic differentials. Generalizing results of Benoist-Hulin, Loftin and Dumas-Wolf, we show that poles of order less than $3$ of cubic differentials correspond to finite volume ends of convex $mathbb{RP}^2$-structures, while poles of order at least $3$ correspond to geodesic or piecewise geodesic boundary components. More specifically, in the latter situation, we prove asymptotic results for the convex $mathbb{RP}^2$-structure around the pole in terms of the cubic differential.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2018-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41379947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Refined disk potentials for immersed Lagrangian surfaces 浸没拉格朗日曲面的精细圆盘势
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2018-06-10 DOI: 10.4310/jdg/1664378618
Georgios Dimitroglou Rizell, T. Ekholm, D. Tonkonog
{"title":"Refined disk potentials for immersed Lagrangian surfaces","authors":"Georgios Dimitroglou Rizell, T. Ekholm, D. Tonkonog","doi":"10.4310/jdg/1664378618","DOIUrl":"https://doi.org/10.4310/jdg/1664378618","url":null,"abstract":"We define a refined Gromov-Witten disk potential of self-transverse monotone immersed Lagrangian surfaces in a symplectic 4-manifold as an element in a capped version of the Chekanov--Eliashberg dg-algebra of the singularity links of the double points (a collection of Legendrian Hopf links). We give a surgery formula that expresses the potential after smoothing a double point. \u0000We study refined potentials of monotone immersed Lagrangian spheres in the complex projective plane and find monotone spheres that cannot be displaced from complex lines and conics by symplectomorphisms. We also derive general restrictions on sphere potentials using Legendrian lifts to the contact 5-sphere.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2018-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44733601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 13
Index theory and deformations of open nonnegatively curved manifolds 开放非负弯曲流形的指标理论与变形
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2018-05-06 DOI: 10.4310/jdg/1669998181
I. Belegradek
{"title":"Index theory and deformations of open nonnegatively curved manifolds","authors":"I. Belegradek","doi":"10.4310/jdg/1669998181","DOIUrl":"https://doi.org/10.4310/jdg/1669998181","url":null,"abstract":"We use an index-theoretic technique of Hitchin to show that the space of complete Riemannian metrics of nonnegative sectional curvature on certain open spin manifolds has nontrivial homotopy groups in infinitely many degrees. A new ingredient of independent interest is homotopy density of the subspace of metrics with cylindrical ends.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2018-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47745625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 1
Minimal planes in asymptotically flat three-manifolds 渐近平坦三流形中的极小平面
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2018-04-16 DOI: 10.4310/jdg/1649953568
L. Mazet, H. Rosenberg
{"title":"Minimal planes in asymptotically flat three-manifolds","authors":"L. Mazet, H. Rosenberg","doi":"10.4310/jdg/1649953568","DOIUrl":"https://doi.org/10.4310/jdg/1649953568","url":null,"abstract":"In this paper, we improve a result by Chodosh and Ketover. We prove that, in an asymptotically flat $3$-manifold $M$ that contains no closed minimal surfaces, fixing $qin M$ and a $2$-plane $V$ in $T_qM$ there is a properly embedded minimal plane $Sigma$ in $M$ such that $qinSigma$ and $T_qSigma=V$. We also prove that fixing three points in $M$ there is a properly embedded minimal plane passing through these three points.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2018-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48580191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 4
Morita equivalence and the generalized Kähler potential Morita等价与广义Kähler势
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2018-04-15 DOI: 10.4310/jdg/1659987891
Francis Bischoff, M. Gualtieri, M. Zabzine
{"title":"Morita equivalence and the generalized Kähler potential","authors":"Francis Bischoff, M. Gualtieri, M. Zabzine","doi":"10.4310/jdg/1659987891","DOIUrl":"https://doi.org/10.4310/jdg/1659987891","url":null,"abstract":"We solve the problem of determining the fundamental degrees of freedom underlying a generalized Kahler structure of symplectic type. For a usual Kahler structure, it is well-known that the geometry ...","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2018-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48637629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 10
Geodesic nets with three boundary vertices 具有三个边界顶点的测地线网
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2018-03-10 DOI: 10.4310/jdg/1631124286
Fabian Parsch
{"title":"Geodesic nets with three boundary vertices","authors":"Fabian Parsch","doi":"10.4310/jdg/1631124286","DOIUrl":"https://doi.org/10.4310/jdg/1631124286","url":null,"abstract":"We prove that a geodesic net with three boundary (= unbalanced) vertices on a non-positively curved plane has at most one balanced vertex. We do not assume any a priori bound for the degrees of unbalanced vertices. The result seems to be new even in the Euclidean case. We demonstrate by examples that the result is not true for metrics of positive curvature on the plane, and that there are no immediate generalizations of this result for geodesic nets with four unbalanced vertices.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2018-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48277955","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 3
On the Frøyshov invariant and monopole Lefschetz number 关于Frøyshov不变量和单极Lefschetz数
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2018-02-21 DOI: 10.4310/jdg/1683307008
Jianfeng Lin, Daniel Ruberman, N. Saveliev
{"title":"On the Frøyshov invariant and monopole Lefschetz number","authors":"Jianfeng Lin, Daniel Ruberman, N. Saveliev","doi":"10.4310/jdg/1683307008","DOIUrl":"https://doi.org/10.4310/jdg/1683307008","url":null,"abstract":"Given an involution on a rational homology 3-sphere $Y$ with quotient the $3$-sphere, we prove a formula for the Lefschetz number of the map induced by this involution in the reduced monopole Floer homology. This formula is motivated by a variant of Witten's conjecture relating the Donaldson and Seiberg--Witten invariants of 4-manifolds. A key ingredient is a skein-theoretic argument, making use of an exact triangle in monopole Floer homology, that computes the Lefschetz number in terms of the Murasugi signature of the branch set and the sum of Fr{o}yshov invariants associated to spin structures on $Y$. We discuss various applications of our formula in gauge theory, knot theory, contact geometry, and 4-dimensional topology.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2018-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46174205","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 18
Algebraic torus actions on contact manifolds 接触流形上的代数环面作用
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2018-02-14 DOI: 10.4310/jdg/1659987892
Jaroslaw Buczy'nski, Jaroslaw A. Wi'sniewski, Andrzej Weber
{"title":"Algebraic torus actions on contact manifolds","authors":"Jaroslaw Buczy'nski, Jaroslaw A. Wi'sniewski, Andrzej Weber","doi":"10.4310/jdg/1659987892","DOIUrl":"https://doi.org/10.4310/jdg/1659987892","url":null,"abstract":"We prove LeBrun-Salamon Conjecture in low dimensions. More precisely, we show that a contact Fano manifold X of dimension 2n+1 that has reductive automorphism group of rank at least n-2 is necessarily homogeneous. This implies that any positive quaternion-Kahler manifold of real dimension at most 16 is necessarily a symmetric space, one of the Wolf spaces. A similar result about contact Fano manifolds of dimension at most 9 with reductive automorphism group also holds. The main difficulty in approaching the conjecture is how to recognize a homogeneous space in an abstract variety. We contribute to such problem in general, by studying the action of algebraic torus on varieties and exploiting Bialynicki-Birula decomposition and equivariant Riemann-Roch theorems. From the point of view of T-varieties (that is, varieties with a torus action), our result is about high complexity T-manifolds. The complexity here is at most (dim X+5)/2 with dim X arbitrarily high, but we require this special (contact) structure of X. Previous methods for studying T-varieties in general usually only apply for complexity at most 2 or 3.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2018-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46260595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 26
首页 上一页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信