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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Curvature flows for almost-hermitian Lie groups
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by Jorge Lauret PDF
Trans. Amer. Math. Soc. 367 (2015), 7453-7480 Request permission

Abstract:

We study curvature flows in the locally homogeneous case (e.g. compact quotients of Lie groups, solvmanifolds, nilmanifolds) in a unified way by considering a generic flow under just a few natural conditions on the broad class of almost-hermitian structures. As a main tool, we use an ODE system defined on the variety of $2n$-dimensional Lie algebras, called the bracket flow, whose solutions differ from those to the original curvature flow by only pull-back by time-dependent diffeomorphisms. The approach, which has already been used to study the Ricci flow on homogeneous manifolds, is useful to better visualize the possible pointed limits of solutions, under diverse rescalings, as well as to address regularity issues. Immortal, ancient and self-similar solutions arise naturally from the qualitative analysis of the bracket flow. The Chern-Ricci flow and the symplectic curvature flow are considered in more detail.
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Additional Information
  • Jorge Lauret
  • Affiliation: Universidad Nacional de Córdoba, FaMAF and CIEM, 5000 Córdoba, Argentina
  • MR Author ID: 626241
  • Email: lauret@famaf.unc.edu.ar
  • Received by editor(s): September 28, 2013
  • Received by editor(s) in revised form: March 19, 2014
  • Published electronically: December 11, 2014
  • Additional Notes: The author’s research was partially supported by grants from CONICET, FONCYT and SeCyT (Universidad Nacional de Córdoba)
  • © Copyright 2014 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 367 (2015), 7453-7480
  • MSC (2010): Primary 53C30, 53C44
  • DOI: https://doi.org/10.1090/S0002-9947-2014-06476-3
  • MathSciNet review: 3378836