Almost CoKähler manifolds satisfying Miao-Tam equation
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The aim of the present paper is to classify almost CoKähler manifolds satisfying Miao-Tam equation. We find the expression of the curvature tensor in an almost CoKähler manifold of dimension greater than 3 with \(\xi \) belonging to the \((k, \mu )\)-nullity distribution and \(k<0\). We prove that gradient of \(\lambda \) is pointwise collinear with \(\xi \). As a consequence, we obtain that the potential function \(\lambda \) is constant. Finally, we show that the solution of the Miao-Tam equation on almost CoKähler manifolds of dimension greater than 3 with \(\xi \) belonging to the \((k, \mu )\)-nullity distribution and \(k<0\) is either trivial or Einstein.
KeywordsHessian Laplacian Miao-Tam equation almost CoKähler manifolds
Mathematics Subject Classification53C15 53C25
The authors are thankful to the reviewer for his/her valuable suggestions for the better improvement of the paper. Also the author Debabrata Kar is supported by CSIR, India (File no: 09/028(1007)/2017-EMR-1).
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