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

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

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]).

Original language	English
Pages (from-to)	391-424
Number of pages	34
Journal	Pacific Journal of Mathematics
Volume	320
Issue number	2
DOIs	https://doi.org/10.2140/pjm.2022.320.391
Publication status	Published - 2023

Keywords

Clifford system
characteristic map
focal submanifold
harmonic map
isoparametric hypersurface
nonnegative sectional curvature

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10.2140/pjm.2022.320.391

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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",

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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

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Keywords

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