Levi‐Civita Ricci‐Flat Doubly Warped Product Hermitian Manifolds

Qihui Ni, Yong He, Jinhua Yang and Hui Zhang

Advances in Mathematical Physics, 2022, vol. 2022, issue 1

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
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2022/2077040

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2022:y:2022:i:1:n:2077040

Access Statistics for this article

More articles in Advances in Mathematical Physics from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().