CLIFFORD SYSTEMS, HARMONIC MAPS AND METRICS WITH NONNEGATIVE CURVATURE

Chao Qian; Zizhou Tang; Wenjiao Yan

doi:10.2140/pjm.2022.320.391

CLIFFORD SYSTEMS, HARMONIC MAPS AND METRICS WITH NONNEGATIVE CURVATURE

Chao Qian^*, Zizhou Tang, Wenjiao Yan

^*此作品的通讯作者

数学学院

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

Associated with a symmetric Clifford system {P₀, P₁,…, P_m} on R^2l, there is a canonical vector bundle η over S^l−1. For m = 4 and 8, we construct explicitly its characteristic map, and determine completely when the sphere bundle S(η) associated to η admits a cross-section. These generalize the results of Steenrod (1951) and James (1958). As an application, we establish new harmonic representatives of certain elements in homotopy groups of spheres (see [Peng and Tang 1997; 1998]).

源语言	英语
页（从-至）	391-424
页数	34
期刊	Pacific Journal of Mathematics
卷	320
期	2
DOI	https://doi.org/10.2140/pjm.2022.320.391
出版状态	已出版 - 2023

访问文件

10.2140/pjm.2022.320.391

其它文件与链接

链接到 Scopus 的出版物

引用此

@article{cf6363fc67a94c0da22b5240f608d6cb,

title = "CLIFFORD SYSTEMS, HARMONIC MAPS AND METRICS WITH NONNEGATIVE CURVATURE",

abstract = "Associated with a symmetric Clifford system {P0, P1,…, Pm} on R2l, there is a canonical vector bundle η over Sl−1. For m = 4 and 8, we construct explicitly its characteristic map, and determine completely when the sphere bundle S(η) associated to η admits a cross-section. These generalize the results of Steenrod (1951) and James (1958). As an application, we establish new harmonic representatives of certain elements in homotopy groups of spheres (see [Peng and Tang 1997; 1998]).",

keywords = "Clifford system, characteristic map, focal submanifold, harmonic map, isoparametric hypersurface, nonnegative sectional curvature",

author = "Chao Qian and Zizhou Tang and Wenjiao Yan",

note = "Publisher Copyright: {\textcopyright} 2022 Mathematical Sciences Publishers",

year = "2023",

doi = "10.2140/pjm.2022.320.391",

language = "English",

volume = "320",

pages = "391--424",

journal = "Pacific Journal of Mathematics",

issn = "0030-8730",

publisher = "Mathematical Sciences Publishers",

number = "2",

}

TY - JOUR

T1 - CLIFFORD SYSTEMS, HARMONIC MAPS AND METRICS WITH NONNEGATIVE CURVATURE

AU - Qian, Chao

AU - Tang, Zizhou

AU - Yan, Wenjiao

PY - 2023

Y1 - 2023

N2 - Associated with a symmetric Clifford system {P0, P1,…, Pm} on R2l, there is a canonical vector bundle η over Sl−1. For m = 4 and 8, we construct explicitly its characteristic map, and determine completely when the sphere bundle S(η) associated to η admits a cross-section. These generalize the results of Steenrod (1951) and James (1958). As an application, we establish new harmonic representatives of certain elements in homotopy groups of spheres (see [Peng and Tang 1997; 1998]).

AB - Associated with a symmetric Clifford system {P0, P1,…, Pm} on R2l, there is a canonical vector bundle η over Sl−1. For m = 4 and 8, we construct explicitly its characteristic map, and determine completely when the sphere bundle S(η) associated to η admits a cross-section. These generalize the results of Steenrod (1951) and James (1958). As an application, we establish new harmonic representatives of certain elements in homotopy groups of spheres (see [Peng and Tang 1997; 1998]).

KW - Clifford system

KW - characteristic map

KW - focal submanifold

KW - harmonic map

KW - isoparametric hypersurface

KW - nonnegative sectional curvature

UR - http://www.scopus.com/inward/record.url?scp=85149665266&partnerID=8YFLogxK

U2 - 10.2140/pjm.2022.320.391

DO - 10.2140/pjm.2022.320.391

M3 - Article

AN - SCOPUS:85149665266

SN - 0030-8730

VL - 320

SP - 391

EP - 424

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

IS - 2

ER -

CLIFFORD SYSTEMS, HARMONIC MAPS AND METRICS WITH NONNEGATIVE CURVATURE

摘要

访问文件

其它文件与链接

指纹

引用此