Abstract
In the present paper, we characterize \((k,\mu )'\)-almost Kenmotsu manifolds admitting \(*\)-critical point equation. It is shown that if \((g, \lambda )\) is a non-constant solution of the \(*\)-critical point equation of a connected non-compact \((k,\mu )'\)-almost Kenmotsu manifold, then (1) the manifold M is locally isometric to \(\mathbb {H}^{n+1}(-4)\)\(\times \)\(\mathbb {R}^n\), (2) the manifold M is \(*\)-Ricci flat and (3) the function \(\lambda \) is harmonic. Finally an illustrative example is presented.
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Acknowledgements
The author Dibakar Dey is supported by the Council of Scientific and Industrial Research, India (File No: 09/028(1010)/2017-EMR-1) in the form of senior research fellowship.
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Dey, D., Majhi, P. \(*\)-Critical point equation on a class of almost Kenmotsu manifolds. J. Geom. 111, 16 (2020). https://doi.org/10.1007/s00022-020-0529-4
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DOI: https://doi.org/10.1007/s00022-020-0529-4
Keywords
- Critical point equation
- \(*\)-Critical point equation
- Almost Kenmotsu manifolds
- \((k, \mu )'\)-Nullity distributions