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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Adapted metrics on locally conformally product manifolds
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by Andrei Moroianu and Mihaela Pilca;
Proc. Amer. Math. Soc. 152 (2024), 2221-2228
DOI: https://doi.org/10.1090/proc/16706
Published electronically: March 7, 2024

Abstract:

We show that the Gauduchon metric $g_0$ of a compact locally conformally product manifold $(M,c,D)$ of dimension greater than $2$ is adapted, in the sense that the Lee form of $D$ with respect to $g_0$ vanishes on the $D$-flat distribution of $M$. We also characterize adapted metrics as critical points of a natural functional defined on the conformal class.
References
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Bibliographic Information
  • Andrei Moroianu
  • Affiliation: Université Paris-Saclay, CNRS, Laboratoire de Mathématiques d’Orsay, 91405 Orsay, France; and Institute of Mathematics “Simion Stoilow” of the Romanian Academy, 21 Calea Grivitei, 010702 Bucharest, Romania
  • MR Author ID: 357089
  • ORCID: 0000-0002-9799-1036
  • Email: andrei.moroianu@math.cnrs.fr
  • Mihaela Pilca
  • Affiliation: Fakultät für Mathematik, Universität Regensburg, Universitätsstr. 31 D-93040 Regensburg, Germany
  • MR Author ID: 936403
  • Email: mihaela.pilca@mathematik.uni-regensburg.de
  • Received by editor(s): May 21, 2023
  • Received by editor(s) in revised form: October 17, 2023
  • Published electronically: March 7, 2024
  • Additional Notes: This work was supported by the Procope Project No. 57650868 (Germany) / 48959TL (France) and by the PNRR Project CF149/31.07.2023.
  • Communicated by: Jiaping Wang
  • © Copyright 2024 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 152 (2024), 2221-2228
  • MSC (2020): Primary 53C18
  • DOI: https://doi.org/10.1090/proc/16706
  • MathSciNet review: 4728485