Please use this identifier to cite or link to this item: https://hdl.handle.net/1959.11/56979
Title: On the Classification of Spherical Rigid CR Manifolds and Sasakian Manifolds in C2
Contributor(s): Sykes, Daniel (author); Schmalz, Gerd  (supervisor)orcid ; Harris, Adam  (supervisor)orcid 
Conferred Date: 2021-10-06
Copyright Date: 2021-09
Handle Link: https://hdl.handle.net/1959.11/56979
Related Research Outputs: https://hdl.handle.net/1959.11/56980
Abstract: 

We consider spherical hypersurfaces in C2 with a fixed Reeb vector field as 3-dimensional Sasakian manifolds. We establish the correspondence between three different sets of parameters, namely, those arising from representing the Reeb vector field as an automorphism of the Heisenberg sphere, the parameters used in Stanton’s description of rigid spheres, and the parameters arising from the rigid normal forms. We also geometrically describe the moduli space for rigid spheres, and provide geometric distinction between Stanton’s hypersurfaces and those found in [17]. We determine the Sasakian automorphism groups of the rigid spheres, detecting the homogeneous Sasakian manifolds amongst them, and we determine the Sasakian automorphisms of the CR manifolds arising in E. Cartan’s classical list of homogeneous CR hypersur- ´ faces. Furthermore, we relax the condition on the Reeb vector field to allow preservation up to a nonzero dilation, called homothetic Sasakian preservation. Finally, we determine the homogeneous Sasakian manifolds with respect to the homothetic Sasakian preservation.

Publication Type: Thesis Masters Research
Fields of Research (FoR) 2008: 010102 Algebraic and Differential Geometry
010111 Real and Complex Functions (incl. Several Variables)
010504 Mathematical Aspects of General Relativity
Socio-Economic Objective (SEO) 2008: 970101 Expanding Knowledge in the Mathematical Sciences
HERDC Category Description: T1 Thesis - Masters Degree by Research
Description: Please contact rune@une.edu.au if you require access to this thesis for the purpose of research or study.
Appears in Collections:School of Science and Technology
Thesis Masters Research

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