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Myers-type compactness theorem with the Bakry-Emery Ricci tensor Bakry-Emery Ricci张量下的myers型紧性定理
IF 0.5 4区 数学
Tohoku Mathematical Journal Pub Date : 2019-04-18 DOI: 10.2748/tmj.20200512
Seungsu Hwang, Sanghun Lee
{"title":"Myers-type compactness theorem with the Bakry-Emery Ricci tensor","authors":"Seungsu Hwang, Sanghun Lee","doi":"10.2748/tmj.20200512","DOIUrl":"https://doi.org/10.2748/tmj.20200512","url":null,"abstract":"In this paper, we first prove the $f$-mean curvature comparison in a smooth metric measure space when the Bakry-Emery Ricci tensor is bounded from below and $|f|$ is bounded. Based on this, we define a Myers-type compactness theorem by generalizing the results of Cheeger, Gromov, and Taylor and of Wan for the Bakry-Emery Ricci tensor. Moreover, we improve a result from Soylu by using a weaker condition on a derivative $f'(t)$.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47372268","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}
引用次数: 0
Invariants of algebraic varieties over imperfect fields 不完全域上代数变量的不变量
IF 0.5 4区 数学
Tohoku Mathematical Journal Pub Date : 2019-03-25 DOI: 10.2748/tmj.20200611
Hiromu Tanaka
{"title":"Invariants of algebraic varieties over imperfect fields","authors":"Hiromu Tanaka","doi":"10.2748/tmj.20200611","DOIUrl":"https://doi.org/10.2748/tmj.20200611","url":null,"abstract":"We introduce four invariants of algebraic varieties over imperfect fields, each of which measures either geometric non-normality or geometric non-reducedness. The first objective of this article is to establish fundamental properties of these invariants. We then apply our results to curves over imperfect fields. In particular, we establish a genus change formula and prove the boundedness of non-smooth regular curves of genus one. We also compute our invariants for some explicit examples.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43904808","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}
引用次数: 13
Some remarks on free arrangements 关于免费安排的一些评论
IF 0.5 4区 数学
Tohoku Mathematical Journal Pub Date : 2019-03-02 DOI: 10.2748/tmj.20200318
Torsten Hoge, G. Röhrle
{"title":"Some remarks on free arrangements","authors":"Torsten Hoge, G. Röhrle","doi":"10.2748/tmj.20200318","DOIUrl":"https://doi.org/10.2748/tmj.20200318","url":null,"abstract":"We exhibit a particular free subarrangement of a certain restriction of the Weyl arrangement of type $E_7$ and use it to give an affirmative answer to a recent conjecture by T.~Abe on the nature of additionally free and stair-free arrangements.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42827814","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}
引用次数: 5
Rational orbits of primitive trivectors in dimension six 六维原始三向量的有理轨道
IF 0.5 4区 数学
Tohoku Mathematical Journal Pub Date : 2019-03-01 DOI: 10.2748/TMJ/1552100441
Akihiko Yukie
{"title":"Rational orbits of primitive trivectors in dimension six","authors":"Akihiko Yukie","doi":"10.2748/TMJ/1552100441","DOIUrl":"https://doi.org/10.2748/TMJ/1552100441","url":null,"abstract":"","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44932521","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}
引用次数: 0
Classification of biharmonic $mathcal{C}$-parallel Legendrian submanifolds in 7-dimensional Sasakian space forms 七维Sasakian空间形式中双调和$mathcal{C}$平行Legendarian子流形的分类
IF 0.5 4区 数学
Tohoku Mathematical Journal Pub Date : 2019-03-01 DOI: 10.2748/TMJ/1552100448
T. Sasahara
{"title":"Classification of biharmonic $mathcal{C}$-parallel Legendrian submanifolds in 7-dimensional Sasakian space forms","authors":"T. Sasahara","doi":"10.2748/TMJ/1552100448","DOIUrl":"https://doi.org/10.2748/TMJ/1552100448","url":null,"abstract":"","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41477898","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}
引用次数: 3
Obstacle problem for Musielak-Orlicz Dirichlet energy integral on metric measure spaces 度量测度空间上Musielak-Orlicz-Dichlet能量积分的障碍问题
IF 0.5 4区 数学
Tohoku Mathematical Journal Pub Date : 2019-03-01 DOI: 10.2748/TMJ/1552100442
F. Maeda, T. Ohno, T. Shimomura
{"title":"Obstacle problem for Musielak-Orlicz Dirichlet energy integral on metric measure spaces","authors":"F. Maeda, T. Ohno, T. Shimomura","doi":"10.2748/TMJ/1552100442","DOIUrl":"https://doi.org/10.2748/TMJ/1552100442","url":null,"abstract":"","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2748/TMJ/1552100442","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45936361","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}
引用次数: 1
Characterization of 2-dimensional normal Mather-Jacobian log canonical singularities 二维正规Mather-Jacobian对数正则奇点的刻画
IF 0.5 4区 数学
Tohoku Mathematical Journal Pub Date : 2019-03-01 DOI: 10.2748/TMJ/1552100445
K. Shibata, Nguyen Duc Tam
{"title":"Characterization of 2-dimensional normal Mather-Jacobian log canonical singularities","authors":"K. Shibata, Nguyen Duc Tam","doi":"10.2748/TMJ/1552100445","DOIUrl":"https://doi.org/10.2748/TMJ/1552100445","url":null,"abstract":"","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43428578","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}
引用次数: 2
Circles in self dual symmetric $R$-spaces 自对偶对称$R$-空间中的圆
IF 0.5 4区 数学
Tohoku Mathematical Journal Pub Date : 2019-02-04 DOI: 10.2748/tmj.20200312
M. Salvai
{"title":"Circles in self dual symmetric $R$-spaces","authors":"M. Salvai","doi":"10.2748/tmj.20200312","DOIUrl":"https://doi.org/10.2748/tmj.20200312","url":null,"abstract":"Self dual symmetric R-spaces have special curves, called circles, introduced by Burstall, Donaldson, Pedit and Pinkall in 2011, whose definition does not involve the choice of any Riemannian metric. We characterize the elements of the big transformation group G of a self dual symmetric R-space M as those diffeomorphisms of M sending circles in circles. Besides, although these curves belong to the realm of the invariants by G, we manage to describe them in Riemannian geometric terms: Given a circle c in M, there is a maximal compact subgroup K of G such that c, except for a projective reparametrization, is a diametrical geodesic in M (or equivalently, a diagonal geodesic in a maximal totally geodesic flat torus of M), provided that M carries the canonical symmetric K-invariant metric. We include examples for the complex quadric and the split standard or isotropic Grassmannians.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44012519","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}
引用次数: 1
A filtration on the higher Chow group of zero cycles on an abelian variety 阿贝尔变换上零环的高Chow群上的滤除
IF 0.5 4区 数学
Tohoku Mathematical Journal Pub Date : 2019-01-14 DOI: 10.2748/tmj.20191030
Buntaro Kakinoki
{"title":"A filtration on the higher Chow group of zero cycles on an abelian variety","authors":"Buntaro Kakinoki","doi":"10.2748/tmj.20191030","DOIUrl":"https://doi.org/10.2748/tmj.20191030","url":null,"abstract":"In this paper we extend Gazaki's results on the Chow groups of abelian varieties to the higher Chow groups. We introduce a Gazaki type filtration on the higher Chow group of zero-cycles on an abelian variety, whose graded quotients are connected to the Somekawa type $K$-group. Via the '{e}tale cycle map, we will compare this filtration with a filtration on the '{e}tale cohomology induced by the Hochschild-Serre spectral sequence. As an application over local fields, we obtain an estimate of the kernel of the reciprocity map.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46704209","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}
引用次数: 0
On infiniteness of integral overconvergent de Rham–Witt cohomology modulo torsion 积分过收敛de Rham-Witt上同模扭转的无穷性
IF 0.5 4区 数学
Tohoku Mathematical Journal Pub Date : 2018-12-10 DOI: 10.2748/tmj/1601085622
Veronika Ertl, Atsushi Shiho
{"title":"On infiniteness of integral overconvergent de Rham–Witt cohomology modulo torsion","authors":"Veronika Ertl, Atsushi Shiho","doi":"10.2748/tmj/1601085622","DOIUrl":"https://doi.org/10.2748/tmj/1601085622","url":null,"abstract":"In this article, we give examples of smooth varieties of positive characteristic whose first integral overconvergent de Rham-Witt cohomology modulo torsion is not finitely generated over the Witt ring of the base field.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2018-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49189423","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}
引用次数: 2
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