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
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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