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Some recent work on biharmonic conformal maps 一些关于双调和共形映射的最新研究
Geometry of Submanifolds Pub Date : 2019-09-10 DOI: 10.1090/conm/756/15209
Ye-Lin Ou
{"title":"Some recent work on biharmonic conformal\u0000 maps","authors":"Ye-Lin Ou","doi":"10.1090/conm/756/15209","DOIUrl":"https://doi.org/10.1090/conm/756/15209","url":null,"abstract":"This note reviews some of the recent work on biharmonic conformal maps (see cite{OC}, Chapter 11, for a detailed survey). It will be focused on biharmonic conformal immersions and biharmonic conformal maps between manifolds of the same dimension and their links to isoparametric functions and Yamabe type equations, though biharmonic morphisms (maps that preserve solutions of bi-Laplace equations), generalized harmonic morphisms (maps that pull back germs of harmonic functions to germs of biharmonic functions), and biharmonic conformal and Riemannian submersions will also be touched.","PeriodicalId":165273,"journal":{"name":"Geometry of Submanifolds","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130363090","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: 0
Lagrangian submanifolds of the complex quadric as Gauss maps of hypersurfaces of spheres 作为球面超曲面高斯映射的复二次曲面的拉格朗日子流形
Geometry of Submanifolds Pub Date : 2019-08-15 DOI: 10.1090/conm/756/15213
J. Veken, Anne Wijffels
{"title":"Lagrangian submanifolds of the complex\u0000 quadric as Gauss maps of hypersurfaces of\u0000 spheres","authors":"J. Veken, Anne Wijffels","doi":"10.1090/conm/756/15213","DOIUrl":"https://doi.org/10.1090/conm/756/15213","url":null,"abstract":"The Gauss map of a hypersurface of a unit sphere $S^{n+1}(1)$ is a Lagrangian immersion into the complex quadric $Q^n$ and, conversely, every Lagrangian submanifold of $Q^n$ is locally the image under the Gauss map of several hypersurfaces of $S^{n+1}(1)$. In this paper, we give explicit constructions for these correspondences and we prove a relation between the principal curvatures of a hypersurface of $S^{n+1}(1)$ and the local angle functions of the corresponding Lagrangian submanifold of $Q^n$. The existence of such a relation is remarkable since the definition of the angle functions depends on the choice of an almost product structure on $Q^n$ and since several hypersurfaces of $S^{n+1}(1)$, with different principal curvatures, correspond to the same Lagrangian submanifold of $Q^n$.","PeriodicalId":165273,"journal":{"name":"Geometry of Submanifolds","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134115769","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
Maximally-warped metrics with harmonic curvature 调和曲率的最大弯曲度规
Geometry of Submanifolds Pub Date : 2018-12-14 DOI: 10.1090/conm/756/15198
A. Derdzinski, P. Piccione
{"title":"Maximally-warped metrics with harmonic\u0000 curvature","authors":"A. Derdzinski, P. Piccione","doi":"10.1090/conm/756/15198","DOIUrl":"https://doi.org/10.1090/conm/756/15198","url":null,"abstract":"We describe the local structure of Riemannian manifolds with harmonic curvature which admit a maximum number, in a well-defined sense, of local warped-product decompositions, and at the same time their Ricci tensor has, at some point, only simple eigenvalues. We also prove that in every given dimension greater than two the local-isometry types of such manifolds form a finite-dimensional moduli space, and a nonempty open subset of this moduli space is realized by complete metrics.","PeriodicalId":165273,"journal":{"name":"Geometry of Submanifolds","volume":"103 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121354865","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 stability and index of minimal submanifolds 最小子流形的稳定性和指数
Geometry of Submanifolds Pub Date : 1900-01-01 DOI: 10.1090/conm/756/15197
Hang Chen
{"title":"On stability and index of minimal\u0000 submanifolds","authors":"Hang Chen","doi":"10.1090/conm/756/15197","DOIUrl":"https://doi.org/10.1090/conm/756/15197","url":null,"abstract":"","PeriodicalId":165273,"journal":{"name":"Geometry of Submanifolds","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122230049","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 isoparametric linear Weingarten hypersurfaces in Riemannian and Lorentzian space forms 黎曼和洛伦兹空间形式的等参线性Weingarten超曲面
Geometry of Submanifolds Pub Date : 1900-01-01 DOI: 10.1090/conm/756/15210
C. Özgür
{"title":"On isoparametric linear Weingarten\u0000 hypersurfaces in Riemannian and Lorentzian space\u0000 forms","authors":"C. Özgür","doi":"10.1090/conm/756/15210","DOIUrl":"https://doi.org/10.1090/conm/756/15210","url":null,"abstract":"","PeriodicalId":165273,"journal":{"name":"Geometry of Submanifolds","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132643781","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: 0
My education in differential geometry and my indebtedness 我的微分几何教育和我的债务
Geometry of Submanifolds Pub Date : 1900-01-01 DOI: 10.1090/conm/756/15205
Bang‐Yen Chen
{"title":"My education in differential geometry and my\u0000 indebtedness","authors":"Bang‐Yen Chen","doi":"10.1090/conm/756/15205","DOIUrl":"https://doi.org/10.1090/conm/756/15205","url":null,"abstract":"","PeriodicalId":165273,"journal":{"name":"Geometry of Submanifolds","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134403501","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: 0
Sesquilinear forms and symmetric spaces 半线性形式和对称空间
Geometry of Submanifolds Pub Date : 1900-01-01 DOI: 10.1090/conm/756/15212
G. Thorbergsson
{"title":"Sesquilinear forms and symmetric\u0000 spaces","authors":"G. Thorbergsson","doi":"10.1090/conm/756/15212","DOIUrl":"https://doi.org/10.1090/conm/756/15212","url":null,"abstract":"","PeriodicalId":165273,"journal":{"name":"Geometry of Submanifolds","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114533505","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: 0
Isometric immersions of surfaces: classical approaches and integrability 曲面的等距浸没:经典方法和可积性
Geometry of Submanifolds Pub Date : 1900-01-01 DOI: 10.1090/conm/756/15203
T. Ivey
{"title":"Isometric immersions of surfaces: classical\u0000 approaches and integrability","authors":"T. Ivey","doi":"10.1090/conm/756/15203","DOIUrl":"https://doi.org/10.1090/conm/756/15203","url":null,"abstract":"","PeriodicalId":165273,"journal":{"name":"Geometry of Submanifolds","volume":"93 5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128923620","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: 0
A class of strictly convex hypersurfaces satisfying Weingarten-type inequalities, I 一类满足weingarten型不等式的严格凸超曲面，1
Geometry of Submanifolds Pub Date : 1900-01-01 DOI: 10.1090/conm/756/15201
L. Giugiuc, Bogdan D. Suceavă
{"title":"A class of strictly convex hypersurfaces\u0000 satisfying Weingarten-type inequalities, I","authors":"L. Giugiuc, Bogdan D. Suceavă","doi":"10.1090/conm/756/15201","DOIUrl":"https://doi.org/10.1090/conm/756/15201","url":null,"abstract":"","PeriodicalId":165273,"journal":{"name":"Geometry of Submanifolds","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129008836","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: 0
Statistical manifolds and their submanifolds. Results on Chen-like invariants 统计流形及其子流形。类陈不变量的结果
Geometry of Submanifolds Pub Date : 1900-01-01 DOI: 10.1090/conm/756/15206
I. Mihai
{"title":"Statistical manifolds and their submanifolds.\u0000 Results on Chen-like invariants","authors":"I. Mihai","doi":"10.1090/conm/756/15206","DOIUrl":"https://doi.org/10.1090/conm/756/15206","url":null,"abstract":"","PeriodicalId":165273,"journal":{"name":"Geometry of Submanifolds","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123964689","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
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