Ph.D. Oral Defense - Omid Makhmali
The Department of Mathematics and Statistics invites you to attend the Ph.D. Oral Defense of听Mr. Omid Makhmali
THESIS TITLE:
Differential geometric aspects of causal structures
ABSTRACT
This thesis is concerned with causal structures, which are defined as a field of tangentially nondegenerate
projective hypersurfaces in the projectivized tangent bundle of a manifold. The local听equivalence problem
of causal structures on manifolds of dimension at least four is solved using Cartan鈥檚 method of equivalence,
leading to an {e}-structure over some principal bundle. It is shown that these structures correspond to
parabolic geometries of type (Dn,P1,2) or (Bn,P1,2) when n 鈮� 4 or (D3,P1,2,3). The essential local invariants
are determined and interpreted geometrically. Several special classes of causal structures are considered
including those that are a lift of pseudo-conformal structures and those referred to as conformally flat causal
structures. A rigidity theorem for conformally flat causal structures over compact manifolds is obtained. A
notion of half-flatness is defined for four dimensional causal structures whose null cones are ruled projective
surfaces, which generalizes the notion of half-flat conformal structures of split signature. A twistorial
construction for conformally flat causal structures and half-flat causal structures is given.
COMMITTEE MEMBERS
DEPUTY CHAIR:
Jacques Hurtubise,听Professor,听Mathematics and Statistics, 平特五不中听
SUPERVISOR:
Niky Kamran,听Professor,听Mathematics and Statistics, 平特五不中
滨狈罢贰搁狈础尝听贰齿础惭滨狈贰搁:
John Toth, Professor,听Mathematics and Statistics, 平特五不中
INTERNAL MEMBER:
Gantumur Tsogtgerel, Associate Professor,听Mathematics and Statistics, 平特五不中
贰齿罢贰搁狈础尝听惭贰惭叠贰搁:
Keshav Dasgupta, Associate听Professor,听Physics, 平特五不中
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