@prefix vivo: .
@prefix edm: .
@prefix dcterms: .
@prefix dc: .
@prefix skos: .
@prefix ns0: .
vivo:departmentOrSchool "Non UBC"@en ;
edm:dataProvider "DSpace"@en ;
dcterms:creator "Lucía Martín-Merchán"@en ;
dcterms:issued "2019-11-03T10:23:06Z"@en, "2019-05-06T14:30"@en ;
dcterms:description "In this talk we explain how to describe pure types of $\\mathrm{Spin}(7)$ structures in terms of spinors and focus on the construction of balanced examples. An $8$-dimensional Riemannian manifold admitting a $\\mathrm{Spin}(7)$ structure determined by a $4$-form $\\Omega$ is spin and the structure can also be described in terms of a spinor $\\eta$. Balanced $\\mathrm{Spin}(7)$ structures are a pure class and are characterized by the equation $(\\ast d\\Omega)\\wedge \\Omega=0$ or, equivalently, by the condition that $\\eta$ is harmonic, that is, $D \\eta=0$ where $D$ is the Dirac operator. For our purposes, the description of balanced structures in terms of spinors turns out to be much simpler. Our examples are products $(N\\times T,g+g_k)$, where $(N,g)$ is a $k$-dimensional nilmanifold endowed with a left-invariant metric, $(T,g_k)$ is an $(8-k)$-dimensional flat torus, and $k=5,6$. Under these assumptions, the presence of a left-invariant balanced $\\mathrm{Spin}(7)$ structure on the product is equivalent to the fact that $(N,g)$ admits a left-invariant non-zero harmonic spinor. For this reason we search left-invariant metrics on $N$ that admit left-invariant harmonic spinors. The results of our investigation are a list of $5$ and $6$-dimensional nilmanifolds that verify this condition, and the description of the set of left-invariant metrics with left-invariant harmonic spinors in the particular case $k=5$."@en ;
edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/72172?expand=metadata"@en ;
dcterms:extent "59.0 minutes"@en ;
dc:format "video/mp4"@en ;
skos:note ""@en, "Author affiliation: Universidad Complutense de Madrid"@en ;
dcterms:spatial "Oaxaca (Mexico : State)"@en ;
edm:isShownAt "10.14288/1.0384906"@en ;
dcterms:language "eng"@en ;
ns0:peerReviewStatus "Unreviewed"@en ;
edm:provider "Vancouver : University of British Columbia Library"@en ;
dcterms:publisher "Banff International Research Station for Mathematical Innovation and Discovery"@en ;
dcterms:rights "Attribution-NonCommercial-NoDerivatives 4.0 International"@en ;
ns0:rightsURI "http://creativecommons.org/licenses/by-nc-nd/4.0/"@en ;
ns0:scholarLevel "Graduate"@en ;
dcterms:isPartOf "BIRS Workshop Lecture Videos (Oaxaca (Mexico : State))"@en ;
dcterms:subject "Mathematics"@en, "Differential Geometry, Geometry, Differential Geometry"@en ;
dcterms:title "A spinorial approach to the construction of balanced Spin(7) manifolds"@en ;
dcterms:type "Moving Image"@en ;
ns0:identifierURI "http://hdl.handle.net/2429/72172"@en .