On the Existence and Stability of Filiform Nilsolitons

dc.contributor.advisor	Michael, Jablonski
dc.contributor.author	Danser, Jordan
dc.contributor.committeeMember	Kujawa, Jonathan
dc.contributor.committeeMember	Mendes, Ricardo
dc.contributor.committeeMember	Ozaydin, Murad
dc.contributor.committeeMember	Fryar, Alisa
dc.date.accessioned	2022-07-27T13:06:25Z
dc.date.available	2022-07-27T13:06:25Z
dc.date.issued	2022-08
dc.date.manuscript	2022-07
dc.description.abstract	This dissertation is concerned with the existence and stability of nilsoliton metrics on filiform Lie algebras. The results are presented in two major components. First, we give new results which preclude the existence of soliton metrics on rank 1 filiform algebras. Most notably, these methods circumvent the need to classify the algebras in each dimension (a major obstacle to the study, to this point). Second, we demonstrate that all soliton metrics on rank 2 filiform algebras are stable. In the course of this, we will develop new approximation techniques, and compute the full curvature tensor of rank 2 filiform algebras. The tables for these curvature tensors are contained in Appendix A.	en_US
dc.identifier.uri	https://hdl.handle.net/11244/335964
dc.language	en_US	en_US
dc.subject	Mathematics.	en_US
dc.subject	Differential Geometry	en_US
dc.subject	Homogeneous Geometry	en_US
dc.subject	Nilpotent Lie Algebras	en_US
dc.thesis.degree	Ph.D.	en_US
dc.title	On the Existence and Stability of Filiform Nilsolitons	en_US
ou.group	Dodge Family College of Arts and Sciences::Department of Mathematics	en_US