Levi-Civita Ricci-Flat Doubly Warped Product Hermitian Manifolds

Qihui Ni, Yong He, Jinhua Yang, Hui Zhang and Mehmet Atçeken

Advances in Mathematical Physics, 2022, vol. 2022, 1-7

Abstract: Let M1,g and M2,h be two Hermitian manifolds. The doubly warped product (abbreviated as DWP) Hermitian manifold of M1,g and M2,h is the product manifold M1×M2 endowed with the warped product Hermitian metric G=f22g+f12h, where f1 and f2 are positive smooth functions on M1 and M2, respectively. In this paper, the formulae of Levi-Civita connection, Levi-Civita curvature, the first Levi-Civita Ricci curvature, and Levi-Civita scalar curvature of the DWP-Hermitian manifold are derived in terms of the corresponding objects of its components. We also prove that if the warped function f1 and f2 are holomorphic, then the DWP-Hermitian manifold is Levi-Civita Ricci-flat if and only if M1,g and M2,h are Levi-Civita Ricci-flat manifolds. Thus, we give an effective way to construct Levi-Civita Ricci-flat DWP-Hermitian manifold.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:2077040

DOI: 10.1155/2022/2077040

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