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On the diagonalization of the Ricci flow on Lie groups


Authors: Jorge Lauret and Cynthia Will
Journal: Proc. Amer. Math. Soc. 141 (2013), 3651-3663
MSC (2010): Primary 53C30, 53C44
DOI: https://doi.org/10.1090/S0002-9939-2013-11813-7
Published electronically: June 25, 2013
MathSciNet review: 3080187
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Abstract: The main purpose of this note is to prove that any basis of a nilpotent Lie algebra for which all diagonal left-invariant metrics have diagonal Ricci tensor necessarily produce quite a simple set of structural constants; namely, the bracket of any pair of elements of the basis must be a multiple of one of them, and only the bracket of disjoint pairs can be a nonzero multiple of the same element. Some applications to the Ricci flow of left-invariant metrics on Lie groups concerning diagonalization are also given.


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Additional Information

Jorge Lauret
Affiliation: FaMAF and CIEM, Universidad Nacional de Córdoba, Córdoba, Argentina
Email: lauret@famaf.unc.edu.ar

Cynthia Will
Affiliation: FaMAF and CIEM, Universidad Nacional de Córdoba, Córdoba, Argentina
Email: cwill@famaf.unc.edu.ar

DOI: https://doi.org/10.1090/S0002-9939-2013-11813-7
Received by editor(s): November 1, 2011
Received by editor(s) in revised form: December 30, 2011
Published electronically: June 25, 2013
Additional Notes: This research was partially supported by grants from CONICET (Argentina) and SeCyT (Universidad Nacional de Córdoba)
Communicated by: Lei Ni
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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