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Title: Circle and torus actions in exceptional holonomy
Author: Fowdar, Udhav
ISNI:       0000 0004 9359 664X
Awarding Body: UCL (University College London)
Current Institution: University College London (University of London)
Date of Award: 2020
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The work in this thesis is an investigation of the geometric structures arising on S 1 and T 2 quotients of manifolds endowed with G2 and Spin(7)-structures. This was motivated by the work of Apostolov and Salamon who studied the circle reduction of G2 manifolds and showed that imposing that the quotient is Kähler leads to a rich geometry. We shall consider the following problems: 1. The S 1 quotient of Spin(7)-structures 2. The Kähler reduction of Spin(7) manifolds with T 2 actions 3. The S 1 -invariant G2 Laplacian flow 4. The SU(2) 2 ×U(1)-invariant G2 Laplacian flow on S 3 ×R 4 Our key results include expressions relating the intrinsic torsion of S 1 -invariant Spin(7)-structures to that of the quotient G2-structures, a new expression for the Ricci curvature of Spin(7)-structures only in terms of the intrinsic torsion, infinitely many new examples of (incomplete) Spin(7) metrics arising as T 2 bundles over Kähler manifolds with trivial canonical bundle, the first example of an inhomogeneous shrinking gradient G2 Laplacian soliton and a local classification of closed SU(2) 2 ×U(1)-invariant G2-structures on S 3 ×R 4.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available