Smooth maps into quaternionic Grassmannians inducing a prescribed 4-form

被引：0

作者：

Datta, Mahuya ^{[1
]}

机构：

[1] Indian Stat Inst, Stat & Math Unit, 203 BT Rd, Kolkata 700108, W Bengal, India

来源：

GEOMETRIAE DEDICATA | 2019年 / 200卷 / 01期

关键词：

Principal bundles; Connections; Quaternionic Grassmannians; Symplectic Pontrjagin forms;

D O I：

10.1007/s10711-018-0363-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let knGk(Hn) be the Stiefel bundle of quaternionic k-frames in Hn over the the quaternionic Grassmannian Gk(Hn). Let sigma denote the first symplectic Pontrjagin form associated with the universal connection on k We show that every 4-form on a smooth manifold M can be induced from sigma by a smooth map f:MGk(Hn) (for sufficiently large k and n) provided there exists a continuous map Gk(Hn) which pulls back the deRham cohomology class of sigma (referred as the symplectic Pontrjagin class of kn) onto that of omega.

引用

页码：105 / 114

页数：10

共 46 条

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