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Journal of Geometry

, 110:4 | Cite as

Almost CoKähler manifolds satisfying Miao-Tam equation

  • Debabrata Kar
  • Pradip Majhi
Article
  • 14 Downloads

Abstract

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.

Keywords

Hessian Laplacian Miao-Tam equation almost CoKähler manifolds 

Mathematics Subject Classification

53C15 53C25 

Notes

Acknowledgements

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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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Pure MathematicsUniversity of CalcuttaKolkataIndia

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