Publication Date
Summer 7-5-2022
Abstract
We prove an Obata-type rigidity result for the first eigenvalue of the sub-Laplacian on a compact seven dimensional quaternionic contact (QC) manifold which satisfies a Lichnerowicz-type bound on its QC-Ricci tensor, and has a non-negative Paneitz P -function. In particular, under the stated conditions, the lowest possible eigenvalue of the sub-Laplacian is achieved if and only if the manifold is QC-equivalent to the standard 3-Sasakian sphere.
Degree Name
Mathematics
Level of Degree
Doctoral
Department Name
Mathematics & Statistics
First Committee Member (Chair)
Dimiter Vassilev
Second Committee Member
Hongnian Huang
Third Committee Member
Stephen Lau
Fourth Committee Member
Sergey Grigorian
Language
English
Document Type
Dissertation
Recommended Citation
Mohamed, Abdelrahman. "The Obata First Eigenvalue Theorem on a Seven Dimensional Quaternionic Contact Manifold." (2022). https://digitalrepository.unm.edu/math_etds/187
