Vanishing theorem for irreducible symmetric spaces of noncompact type

被引：0

作者：

Liu, Xu Sheng ^{[1
]}

机构：

[1] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2010年 / 26卷 / 02期

关键词：

vanishing theorem; symmetric space; harmonic form; HARMONIC MAPS; MANIFOLDS; CURVATURE;

D O I：

10.1007/s10114-010-6698-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the following vanishing theorem. Let M be an irreducible symmetric space of noncompact type whose dimension exceeds 2 and M not equal SO (0)(2, 2)/SO(2) x SO(2). Let pi: E -> M be any vector bundle. Then any E-valued L (2) harmonic 1-form over M vanishes. In particular we get the vanishing theorem for harmonic maps from irreducible symmetric spaces of noncompact type.

引用

页码：361 / 368

页数：8

共 7 条

[1]

[Anonymous], 2001, DIFFERENTIAL GEOMETR

[2] THE DIFFERENTIAL FORM SPECTRUM OF MANIFOLDS OF POSITIVE CURVATURE [J].

ESCOBAR, JF ;

FREIRE, A .

DUKE MATHEMATICAL JOURNAL, 1993, 69 (01) :1-41

[3]

Jost J, 2000, J REINE ANGEW MATH, V525, P95

[4]

SAMPSON JH, 1982, I NAZL ALTA MATH S M, pR26

[5] HARMONIC MAPS OF BOUNDED SYMMETRICAL DOMAINS [J].

XIN, YL .

MATHEMATISCHE ANNALEN, 1995, 303 (03) :417-433

[6] Harmonic maps from Kahler manifolds [J].

Xin, YL .

ACTA MATHEMATICA SINICA-ENGLISH SERIES, 1999, 15 (02) :277-292

[7] Curvature estimates for irreducible symmetric spaces [J].

Xusheng Liu .

CHINESE ANNALS OF MATHEMATICS SERIES B, 2006, 27 (03) :287-302

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