## Proceedings of the International Conference on Geometry, Integrability and Quantization

### A Harmonic Endomorphism in a Semi-Riemannian Context

#### Abstract

On the total space of the cotangent bundle $T^{*}M$ of a Riemannian manifold $(M,h)$ we consider the natural Riemann extension $\bar{g}$ with respect to the Levi-Civita connection of $h$. In this setting, we construct on $T^{*}M$ a new para-complex structure $P$, whose harmonicity with respect to $\bar{g}$ is characterized here by using the reduction of $\bar{g}$ to the (classical) Riemann extension.

#### Article information

Dates
First available in Project Euclid: 15 December 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1450194156

Digital Object Identifier
doi:10.7546/giq-17-2016-172-181

Mathematical Reviews number (MathSciNet)
MR3445429

Zentralblatt MATH identifier
06608030

#### Citation

Bejan, Cornelia-Livia; Eken, Şemsi. A Harmonic Endomorphism in a Semi-Riemannian Context. Proceedings of the Seventeenth International Conference on Geometry, Integrability and Quantization, 172--181, Avangard Prima, Sofia, Bulgaria, 2016. doi:10.7546/giq-17-2016-172-181. https://projecteuclid.org/euclid.pgiq/1450194156