THE CANONICAL EIGHT-FORM ON MANIFOLDS WITH HOLONOMY GROUP SPIN(9)

被引：7

作者：

Castrillon Lopez, M. ^{[1
]}

Gadea, P. M. ^{[2
]}

Mykytyuk, I. V. ^{[3
]}

机构：

[1] Univ Complutense Madrid, Fac Matemat, Dept Geometria & Topol, ICMAT CSIC UAM UCM UC3M, E-28040 Madrid, Spain

[2] CSIC, Inst Fis Fundamental, E-28006 Madrid, Spain

[3] Inst Appl Problems Mech & Math, UA-79060 Lvov, Ukraine

来源：

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS | 2010年 / 7卷 / 07期

关键词：

Canonical 8-form on a Spin(9)-manifold; curvature tensor of the Cayley planes; basic spin representation of Spin(9); PROJECTIVE PLANE; CAYLEY OCTAVES; BUNDLES; SPACES;

D O I：

10.1142/S0219887810004786

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

An explicit expression of the canonical 8-form on a Riemannian manifold with a Spin(9)structure, in terms of the nine local symmetric involutions involved, is given. The list of explicit expressions of all the canonical forms related to Berger's list of holonomy groups is thus completed. Moreover, some results on Spin(9)-structures as G-structures defined by a tensor and on the curvature tensor of the Cayley planes, are obtained.

引用

页码：1159 / 1183

页数：25

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