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Minimal Maslov number of R-spaces canonically embedded in Einstein-Kähler C-spaces 最小马斯洛夫数r -空间通常嵌入Einstein-Kähler c -空间
IF 0.5
Complex Manifolds Pub Date : 2019-01-01 DOI: 10.1515/coma-2019-0016
Y. Ohnita
{"title":"Minimal Maslov number of R-spaces canonically embedded in Einstein-Kähler C-spaces","authors":"Y. Ohnita","doi":"10.1515/coma-2019-0016","DOIUrl":"https://doi.org/10.1515/coma-2019-0016","url":null,"abstract":"Abstract An R-space is a compact homogeneous space obtained as an orbit of the isotropy representation of a Riemannian symmetric space. It is known that each R-space has the canonical embedding into a Kähler C-space as a real form, and thus a compact embedded totally geodesic Lagrangian submanifold. The minimal Maslov number of Lagrangian submanifolds in symplectic manifolds is one of invariants under Hamiltonian isotopies and very fundamental to study the Floer homology for intersections of Lagrangian submanifolds. In this paper we show a Lie theoretic formula for the minimal Maslov number of R-spaces canonically embedded in Einstein-Kähler C-spaces, and provide some examples of the calculation by the formula.","PeriodicalId":42393,"journal":{"name":"Complex Manifolds","volume":"6 1","pages":"303 - 319"},"PeriodicalIF":0.5,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/coma-2019-0016","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48128817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
On curvature tensors of Norden and metallic pseudo-Riemannian manifolds 关于Norden和金属伪黎曼流形的曲率张量
IF 0.5
Complex Manifolds Pub Date : 2019-01-01 DOI: 10.1515/coma-2019-0008
A. Blaga, Antonella Nannicini
{"title":"On curvature tensors of Norden and metallic pseudo-Riemannian manifolds","authors":"A. Blaga, Antonella Nannicini","doi":"10.1515/coma-2019-0008","DOIUrl":"https://doi.org/10.1515/coma-2019-0008","url":null,"abstract":"Abstract We study some properties of curvature tensors of Norden and, more generally, metallic pseudo-Riemannian manifolds. We introduce the notion of J-sectional and J-bisectional curvature of a metallic pseudo-Riemannian manifold (M, J, g) and study their properties.We prove that under certain assumptions, if the manifold is locally metallic, then the Riemann curvature tensor vanishes. Using a Norden structure (J, g) on M, we consider a family of metallic pseudo-Riemannian structures {Ja,b}a,b∈ℝ and show that for a ≠ 0, the J-sectional and J-bisectional curvatures of M coincide with the Ja,b-sectional and Ja,b-bisectional curvatures, respectively. We also give examples of Norden and metallic structures on ℝ2n.","PeriodicalId":42393,"journal":{"name":"Complex Manifolds","volume":"6 1","pages":"150 - 159"},"PeriodicalIF":0.5,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/coma-2019-0008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46850043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 15
Differential geometry of Hilbert schemes of curves in a projective space 射影空间中曲线的Hilbert格式的微分几何
IF 0.5
Complex Manifolds Pub Date : 2019-01-01 DOI: 10.1515/coma-2019-0018
R. Bielawski, Carolin Peternell
{"title":"Differential geometry of Hilbert schemes of curves in a projective space","authors":"R. Bielawski, Carolin Peternell","doi":"10.1515/coma-2019-0018","DOIUrl":"https://doi.org/10.1515/coma-2019-0018","url":null,"abstract":"Abstract We describe the natural geometry of Hilbert schemes of curves in ℙ3and, in some cases, in ℙn, n ≥ 4.","PeriodicalId":42393,"journal":{"name":"Complex Manifolds","volume":"6 1","pages":"335 - 347"},"PeriodicalIF":0.5,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/coma-2019-0018","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47549330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
On the Kähler-likeness on almost Hermitian manifolds 关于几乎Hermitian流形上的Kähler相似性
IF 0.5
Complex Manifolds Pub Date : 2019-01-01 DOI: 10.1515/coma-2019-0020
Masaya Kawamura
{"title":"On the Kähler-likeness on almost Hermitian manifolds","authors":"Masaya Kawamura","doi":"10.1515/coma-2019-0020","DOIUrl":"https://doi.org/10.1515/coma-2019-0020","url":null,"abstract":"Abstract We define a Kähler-like almost Hermitian metric. We will prove that on a compact Kähler-like almost Hermitian manifold (M2n, J, g), if it admits a positive ∂ ̄∂-closed (n − 2, n − 2)-form, then g is a quasi-Kähler metric.","PeriodicalId":42393,"journal":{"name":"Complex Manifolds","volume":"6 1","pages":"366 - 376"},"PeriodicalIF":0.5,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/coma-2019-0020","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49512297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Nearly Sasakian manifolds revisited 近sasaki流形重新审视
IF 0.5
Complex Manifolds Pub Date : 2019-01-01 DOI: 10.1515/coma-2019-0017
Beniamino Cappelletti-Montano, Antonio de Nicola, G. Dileo, I. Yudin
{"title":"Nearly Sasakian manifolds revisited","authors":"Beniamino Cappelletti-Montano, Antonio de Nicola, G. Dileo, I. Yudin","doi":"10.1515/coma-2019-0017","DOIUrl":"https://doi.org/10.1515/coma-2019-0017","url":null,"abstract":"Abstract We provide a new, self-contained and more conceptual proof of the result that an almost contact metric manifold of dimension greater than 5 is Sasakian if and only if it is nearly Sasakian.","PeriodicalId":42393,"journal":{"name":"Complex Manifolds","volume":"6 1","pages":"320 - 334"},"PeriodicalIF":0.5,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/coma-2019-0017","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45061050","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Controlled Reeb dynamics — Three lectures not in Cala Gonone 可控Reeb动力学——不在Cala Gonone的三堂课
IF 0.5
Complex Manifolds Pub Date : 2019-01-01 DOI: 10.1515/coma-2019-0006
H. Geiges
{"title":"Controlled Reeb dynamics — Three lectures not in Cala Gonone","authors":"H. Geiges","doi":"10.1515/coma-2019-0006","DOIUrl":"https://doi.org/10.1515/coma-2019-0006","url":null,"abstract":"Abstract These are notes based on a mini-course at the conference RIEMain in Contact, held in Cagliari, Sardinia, in June 2018. The main theme is the connection between Reeb dynamics and topology. Topics discussed include traps for Reeb flows, plugs for Hamiltonian flows, the Weinstein conjecture, Reeb flows with finite numbers of periodic orbits, and global surfaces of section for Reeb flows. The emphasis is on methods of construction, e.g. contact cuts and lifting group actions in Boothby–Wang bundles, that might be useful for other applications in contact topology.","PeriodicalId":42393,"journal":{"name":"Complex Manifolds","volume":"6 1","pages":"118 - 137"},"PeriodicalIF":0.5,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/coma-2019-0006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44183672","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Ricci-flat and Einstein pseudoriemannian nilmanifolds Ricci平面与Einstein伪黎曼幂流形
IF 0.5
Complex Manifolds Pub Date : 2018-12-04 DOI: 10.1515/coma-2019-0010
D. Conti, F. Rossi
{"title":"Ricci-flat and Einstein pseudoriemannian nilmanifolds","authors":"D. Conti, F. Rossi","doi":"10.1515/coma-2019-0010","DOIUrl":"https://doi.org/10.1515/coma-2019-0010","url":null,"abstract":"Abstract This is partly an expository paper, where the authors’ work on pseudoriemannian Einstein metrics on nilpotent Lie groups is reviewed. A new criterion is given for the existence of a diagonal Einstein metric on a nice nilpotent Lie group. Classifications of special classes of Ricci-˛at metrics on nilpotent Lie groups of dimension [eight.tf] are obtained. Some related open questions are presented.","PeriodicalId":42393,"journal":{"name":"Complex Manifolds","volume":"6 1","pages":"170 - 193"},"PeriodicalIF":0.5,"publicationDate":"2018-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/coma-2019-0010","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46692702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 17
On the degeneration of the Frölicher spectral sequence and small deformations 关于Frölicher谱序列的退化和小变形
IF 0.5
Complex Manifolds Pub Date : 2018-11-30 DOI: 10.1515/coma-2020-0003
Michele Maschio
{"title":"On the degeneration of the Frölicher spectral sequence and small deformations","authors":"Michele Maschio","doi":"10.1515/coma-2020-0003","DOIUrl":"https://doi.org/10.1515/coma-2020-0003","url":null,"abstract":"Abstract We study the behavior of the degeneration at the second step of the Frölicher spectral sequence of a 𝒞∞ family of compact complex manifolds. Using techniques from deformation theory and adapting them to pseudo-differential operators we prove a result à la Kodaira-Spencer for the dimension of the second step of the Frölicher spectral sequence and we prove that, under a certain hypothesis, the degeneration at the second step is an open property under small deformations of the complex structure.","PeriodicalId":42393,"journal":{"name":"Complex Manifolds","volume":"7 1","pages":"62 - 72"},"PeriodicalIF":0.5,"publicationDate":"2018-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/coma-2020-0003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47681660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Locally conformally Kähler solvmanifolds: a survey 局部共形Kähler溶剂流形：综述
IF 0.5
Complex Manifolds Pub Date : 2018-11-22 DOI: 10.1515/coma-2019-0003
A. Andrada, M. Origlia
{"title":"Locally conformally Kähler solvmanifolds: a survey","authors":"A. Andrada, M. Origlia","doi":"10.1515/coma-2019-0003","DOIUrl":"https://doi.org/10.1515/coma-2019-0003","url":null,"abstract":"Abstract A Hermitian structure on a manifold is called locally conformally Kähler (LCK) if it locally admits a conformal change which is Kähler. In this survey we review recent results of invariant LCK structures on solvmanifolds and present original results regarding the canonical bundle of solvmanifolds equipped with a Vaisman structure, that is, a LCK structure whose associated Lee form is parallel.","PeriodicalId":42393,"journal":{"name":"Complex Manifolds","volume":"6 1","pages":"65 - 87"},"PeriodicalIF":0.5,"publicationDate":"2018-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/coma-2019-0003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48881027","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Contact Structures of Sasaki Type and Their Associated Moduli Sasaki型接触结构及其相关模
IF 0.5
Complex Manifolds Pub Date : 2018-10-17 DOI: 10.1515/coma-2019-0001
C. Boyer
{"title":"Contact Structures of Sasaki Type and Their Associated Moduli","authors":"C. Boyer","doi":"10.1515/coma-2019-0001","DOIUrl":"https://doi.org/10.1515/coma-2019-0001","url":null,"abstract":"Abstract This article is based on a talk at the RIEMain in Contact conference in Cagliari, Italy in honor of the 78th birthday of David Blair one of the founders of modern Riemannian contact geometry. The present article is a survey of a special type of Riemannian contact structure known as Sasakian geometry. An ultimate goal of this survey is to understand the moduli of classes of Sasakian structures as well as the moduli of extremal and constant scalar curvature Sasaki metrics, and in particular the moduli of Sasaki-Einstein metrics.","PeriodicalId":42393,"journal":{"name":"Complex Manifolds","volume":"6 1","pages":"1 - 30"},"PeriodicalIF":0.5,"publicationDate":"2018-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/coma-2019-0001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45179629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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