Abstract
The paper attempts to introduce and study \(*\)-general critical equation in the frame of \(\alpha\)-cosymplectic manifold. It is proved that if an \(\alpha\)-cosymplectic manifold admits the \(*\)-general critical equation with a non trivial solution (\(\lambda ,g\)), then either \(M^{2n+1}\) is Einstein, or \(M^{2n+1}\) is locally the product of a Kähler manifold and an unit circle \(S^{1}\) or interval. Finally, an example of \(\alpha\) -cosymplectic manifold admitting \(*\)-general critical equation is discussed.
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Acknowledgements
We gratefully acknowledge the constructive comments from the editor and the anonymous referees. Also, the second named author gratefully acknowledge to UGC,F.No. 16-6(DEC.2018)/2019(NET/CSIR) and UGC-Ref.No. 1147/(CSIR-UGC NET DEC. 2018) for financial assistance.
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Baishya, K.K., Bakshi, M.R. Critical metric equation on \(\alpha\)-cosymplectic manifold. J Anal 31, 871–880 (2023). https://doi.org/10.1007/s41478-022-00480-4
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DOI: https://doi.org/10.1007/s41478-022-00480-4