Some Remarks Concerning Anti-Hermitian Metrics

  • Arif Salimov
  • Shabnam AzizovaEmail author


We show that if a torsion tensor of anti-Hermitian metric connection is pure, then the given anti-Hermitian manifold is anti-Kähler. We prove that if an anti-Hermitian manifold is a conformally flat anti-Kähler–Codazzi manifold, then the scalar curvature vanishes, if and only if the given manifold is isotropic anti-Kähler. We also consider anti-Hermitian metrics of Hessian type defined by holomorphic Hamiltonian functions. Finally, we consider an example of anti-Kähler metrics on Walker 4-manifold.


Anti-Kähler–Codazzi manifold isotropic anti-Kähler manifold holomorphic function metric connection with torsion Walker metric 

Mathematics Subject Classification

53C15 53C56 



The authors would like to express their gratitude to the referee for valuable suggestions and comments.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Algebra and GeometryBaku State UniversityBakuAzerbaijan

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