A gap theorem for half-conformally-flat 4-manifolds / Citoler-Saumell, Martin.

Citoler-Saumell, Martin, author.
[Philadelphia, Pennsylvania] : University of Pennsylvania ; Ann Arbor : ProQuest Dissertations & Theses, 2016.
1 online resource (94 pages)
Local subjects:
Mathematics -- Penn dissertations.
Penn dissertations -- Mathematics.
System Details:
Mode of access: World Wide Web.
Given a smooth, compact manifold, an important question to ask is, what are the "best'' metrics that it admits. A reasonable approach is to consider as "best'' metrics those that have the least amount of curvature possible. This leads to the study of canonical metrics, that are defined as minimizers of several scale-invariant Riemannian functionals. In this dissertation, we study the minimizers of the Weyl curvature functional in dimension four, which are precisely half-conformally-flat metrics. Extending a result of LeBrun, we show an obstruction to the existence of "almost'' scalar-flat half-conformally-flat metrics in terms of the positive-definite part of its intersection form. On a related note, we prove a removable singularity result for Hodge-harmonic self-dual 2-forms on compact, anti-self-dual Riemannian orbifolds with non-negative scalar curvature.
Source: Dissertation Abstracts International, Volume: 78-07(E), Section: B.
Advisors: Brian J. Weber; Committee members: Christopher B. Croke; Brian J. Weber; Wolfgang Ziller.
Department: Mathematics.
Ph.D. University of Pennsylvania 2016.
Local notes:
School code: 0175
Weber, Brian J., degree supervisor.
Ziller, Wolfgang, degree committee member.
Weber, Brian J., degree committee member.
Croke, Christopher B., degree committee member.
University of Pennsylvania. Mathematics, degree granting institution.
Contained In:
Dissertation Abstracts International 78-07B(E).
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Restricted for use by site license.
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