Variation formulae for the volume of coassociative submanifolds
type: Item
instance of: scholarly article
title: Variation formulae for the volume of coassociative submanifolds
author: Tommaso Pacini
author: Alberto Raffero
published in: Annals of Global Analysis and Geometry
publication date: 2024-06-10T00:00:00Z
review text: The paper under review deals with the calculus of variations of the volume functional for submanifolds, in a specific geometric context. More precisely, the purpose of this paper is to show how the above plays out in the context of \(G_2\) geometry: one deals with 7-dimensional manifolds endowed with a certain non-degenerate closed 3-form \(\phi\). The authors discuss the analogy between \(G_2\) and Kähler geometry, and point out the differences between them.\par The main result is a new second variation formula, specific to coassociative submanifolds. One standard goal of such a formula is to allow to detect geometric conditions ensuring that a minimal submanifold is also stable. The authors find sufficient conditions.\par The new formulae are illustrated with several examples, both homogeneous and non-homogeneoues.
reviewed by: Ion Mihai
Mathematics Subject Classification ID: 53C38
Mathematics Subject Classification ID: 53C29
zbMATH DE Number: 7862367
zbMATH Keywords: \(\mathrm{G2}\)-manifolds
zbMATH Keywords: coassociative submanifolds
zbMATH Keywords: volume variation formulae
MaRDI profile type: Publication
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DOI: 10.1007/S10455-024-09955-Y
description: scientific article; zbMATH DE number 7862367