Proceedings of the International Conference on Geometry, Integrability and Quantization

A Harmonic Endomorphism in a Semi-Riemannian Context

Cornelia-Livia Bejan and Şemsi Eken

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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

Source
Proceedings of the Seventeenth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov, Guowu Meng and Akira Yoshioka, eds. (Sofia: Avangard Prima, 2016), 172-181

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


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