On complex Riemannian foliations

23rd International Conference on Integrable Systems and Quantum Symmetries

Ida, Cristian^1

Department of Mathematics and Computer Science, University Transilvania of Braov, Str. Iuliu Maniu 50, Braov

500091, Romania^1

关键词: Einstein equations;    Riemannian metrics;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/670/1/012025/pdf
DOI  :  10.1088/1742-6596/670/1/012025

来源: IOP

【 摘 要 】

In this paper we make some general considerations about the geometry of complex Riemannian foliations, we introduce a leafwise characteristic connection and we write Einstein equations with respect to it. Next, using an one-to-one correspondence between leafwise holomorphic Riemannian metrics and leafwise anti-Kählerian metrics, we focus on the Einstein condition for a leafwise holomorphic Riemannian metric and the associated real leafwise anti-Kählerian metric on a manifold endowed with a complex foliation.