Real geometric invariant theory and Ricci soliton metrics on two-step nilmanifolds

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  • March 22, 2019
Creator
  • Jablonski, Michael R.
    • Affiliation: College of Arts and Sciences, Department of Mathematics
Abstract
  • In this work we study Real Geometric Invariant Theory and its applications to leftinvariant geometry of nilpotent Lie groups. We develop some new results in the real category that distinguish GIT over the reals from GIT over the complexes. Moreover, we explore some of the basic relationships between real and complex GIT over projective space to obtain analogues of the well-known relationships that previously existed in the affine setting. This work is applied to the problem of finding left-invariant Ricci soliton metrics on two-step nilpotent Lie groups. Using our work on Real GIT, we show that most two-step nilpotent Lie groups admit left-invariant Ricci soliton metrics. Moreover, we build many new families of nilpotent Lie groups which cannot admit such metrics.
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  • In Copyright
Advisor
  • Eberlein, Patrick
Degree granting institution
  • University of North Carolina at Chapel Hill
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  • Open access
Date uploaded
  • October 19, 2010

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