A circle quotient of a G<inf>2</inf> cone

Loading...
Thumbnail Image

Date

2020-12-01

Journal Title

Journal ISSN

Volume Title

Repository Usage Stats

94
views
18
downloads

Citation Stats

Abstract

© 2020 A study is made of R6 as a singular quotient of the conical space R+×CP3 with holonomy G2, with respect to an obvious action by U(1) on CP3 with fixed points. Closed expressions are found for the induced metric, and for both the curvature and symplectic 2-forms characterizing the reduction. All these tensors are invariant by a diagonal action of SO(3) on R6, which can be used effectively to describe the resulting geometrical features.

Department

Description

Provenance

Subjects

Citation

Published Version (Please cite this version)

10.1016/j.difgeo.2020.101681

Publication Info

Bryant, Robert, Bobby Acharya and Simon Salamon (2020). A circle quotient of a G2 cone. Differential Geometry and its Application, 73. pp. 101681–101681. 10.1016/j.difgeo.2020.101681 Retrieved from https://hdl.handle.net/10161/21875.

This is constructed from limited available data and may be imprecise. To cite this article, please review & use the official citation provided by the journal.

Scholars@Duke

Bryant

Robert Bryant

Phillip Griffiths Professor of Mathematics

My research concerns problems in the geometric theory of partial differential equations.  More specifically, I work on conservation laws for PDE, Finsler geometry, projective geometry, and Riemannian geometry, including calibrations and the theory of holonomy.

Much of my work involves or develops techniques for studying systems of partial differential equations that arise in geometric problems.  Because of their built-in invariance properties, these systems often have special features that make them difficult to treat by the standard tools of analysis, and so my approach uses ideas and techniques from the theory of exterior differential systems, a collection of tools for analyzing such PDE systems that treats them in a coordinate-free way, focusing instead on their properties that are invariant under diffeomorphism or other transformations.

I’m particularly interested in geometric structures constrained by natural conditions, such as Riemannian manifolds whose curvature tensor satisfies some identity or that supports some additional geometric structure, such as a parallel differential form or other geometric structures that satisfy some partial integrability conditions and in constructing examples of such geometric structures, such as Finsler metrics with constant flag curvature.

I am also the Director of the Simons Collaboration Special Holonomy in Geometry, Analysis, and Physics, and a considerable focus of my research and that of my students is directed towards problems in this area.


Unless otherwise indicated, scholarly articles published by Duke faculty members are made available here with a CC-BY-NC (Creative Commons Attribution Non-Commercial) license, as enabled by the Duke Open Access Policy. If you wish to use the materials in ways not already permitted under CC-BY-NC, please consult the copyright owner. Other materials are made available here through the author’s grant of a non-exclusive license to make their work openly accessible.