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Some remarks on almost Hermitian functionals

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Abstract

We study critical points of natural functionals on various spaces of almost Hermitian structures on a compact manifold \(M^{2n}\). We present a general framework, introducing the notion of gradient of an almost Hermitian functional. As a consequence of the diffeomorphism invariance, we show that a Schur’s type theorem still holds for general almost Hermitian functionals, generalizing a known fact for Riemannian functionals. We present two concrete examples, the Gauduchon’s functional and a close relative of it. These functionals have been studied previously, but not in the most general setup as we do here, and we make some new observations about their critical points.

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Notes

  1. We use Einstein’s convention, that is, repeated index sums.

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Acknowledgements

The second author (CS) has been supported by The Scientific and Research Council of Turkey (TUBITAK) to conduct this research under the TUBITAK-2219-International Postdoctoral Research Fellowship Program for Turkish Citizens with the project number 1059B192000164. Both authors would like to thank Giovanni Russo and Weiyi Zhang for useful comments.

Funding

The second author, Cem Sayar, has been supported by The Scientific and Research Council of Turkey (TUBITAK) to conduct this research under the TUBITAK-2219-International Postdoctoral Research Fellowship Program for Turkish Citizens with the project number 1059B192000164.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Florida International University, Miami, FL, 33199, USA

    Tedi Draghici & Cem Sayar

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  1. Tedi Draghici
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  2. Cem Sayar
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We jointly did the work and wrote the paper.

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Correspondence to Tedi Draghici.

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Dedicated to Professor David E. Blair.

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Draghici, T., Sayar, C. Some remarks on almost Hermitian functionals. Ann Glob Anal Geom 65, 13 (2024). https://doi.org/10.1007/s10455-023-09943-8

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