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VOL. 17 | 2016 A Harmonic Endomorphism in a Semi-Riemannian Context
Cornelia-Livia Bejan, Şemsi Eken

Editor(s) Ivaïlo M. Mladenov, Guowu Meng, Akira Yoshioka

## 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.

## Information

Published: 1 January 2016
First available in Project Euclid: 15 December 2015

zbMATH: 1401.53021
MathSciNet: MR3445429

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