Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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GEOMETRY OF GENERALIZED BERGER-TYPE DEFORMED METRIC ON B-MANIFOLD

  • Received : 2023.03.03
  • Accepted : 2023.06.26
  • Published : 2023.10.31
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Abstract

Let (M2m, 𝜑, g) be a B-manifold. In this paper, we introduce a new class of metric on (M2m, 𝜑, g), obtained by a non-conformal deformation of the metric g, called a generalized Berger-type deformed metric. First we investigate the Levi-Civita connection of this metric. Secondly we characterize the Riemannian curvature, the sectional curvature and the scalar curvature. Finally, we study the proper biharmonicity of the identity map and of a curve on M with respect to a generalized Berger-type deformed metric.

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Acknowledgement

The author expresses his gratitude to the referee for his valuable comments and suggestions towards the improvement of the paper. The author would also like to thank Prof. Ahmed Mohammed Cherif, University Mustapha Stambouli of Mascara for his helpful suggestions and valuable comments.

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