Variation formulae for the volume of coassociative submanifolds

IF 0.6 3区数学 Q3 MATHEMATICS

Annals of Global Analysis and Geometry Pub Date : 2024-04-29 DOI:10.1007/s10455-024-09955-y

Tommaso Pacini, Alberto Raffero

引用次数: 0

Abstract

We prove new variation formulae for the volume of coassociative submanifolds, expressed in terms of \(G_2\) data. These formulae highlight the role of the ambient torsion and Ricci curvature. As a special case, we obtain a second variation formula for variations within the moduli space of coassociative submanifolds. These results apply, for example, to coassociative fibrations. We illustrate our formulae with several examples, both homogeneous and non.

查看原文本刊更多论文

共轭子实体体积的变化公式

我们证明了用\(G_2\)数据表示的共协亚曼形体体积的新变化公式。这些公式突出了环境扭转和里奇曲率的作用。作为特例，我们得到了共协次曼形模空间内变化的第二个变化公式。这些结果适用于共轭纤度等。我们用几个同质和非同质的例子来说明我们的公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Annals of Global Analysis and Geometry 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal examines global problems of geometry and analysis as well as the interactions between these fields and their application to problems of theoretical physics. It contributes to an enlargement of the international exchange of research results in the field. The areas covered in Annals of Global Analysis and Geometry include: global analysis, differential geometry, complex manifolds and related results from complex analysis and algebraic geometry, Lie groups, Lie transformation groups and harmonic analysis, variational calculus, applications of differential geometry and global analysis to problems of theoretical physics.