Year 2020, Volume 13 , Issue 1, Pages 41 - 49 2020-01-30

Harmonic Aspects in an $\eta$-Ricci Soliton

Adara-monica BLAGA [1]


We characterize the $\eta$-Ricci solitons $(g,\xi,\lambda,\mu)$ for the special cases when the $1$-form $\eta$, which is the $g$-dual of $\xi$, is a harmonic or a Schr\"{o}dinger-Ricci harmonic form. We also provide necessary and sufficient conditions for $\eta$ to be a solution of the Schr\"{o}dinger-Ricci equation and point out the relation between the three notions in our context. In particular, we apply these results to a perfect fluid spacetime and using Bochner-Weitzenb\"{o}ck techniques, we formulate some more conclusions for the case of gradient solitons and deduce topological properties of the manifold and its universal covering.


gradient Ricci solitons, Schrödinger-Ricci equation, harmonic form
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Primary Language en
Subjects Mathematics
Journal Section Research Article
Authors

Orcid: 0000-0003-0237-3866
Author: Adara-monica BLAGA (Primary Author)
Institution: West University of Timisoara
Country: Romania


Dates

Publication Date : January 30, 2020

Bibtex @research article { iejg573919, journal = {International Electronic Journal of Geometry}, issn = {}, eissn = {1307-5624}, address = {}, publisher = {Kazım İLARSLAN}, year = {2020}, volume = {13}, pages = {41 - 49}, doi = {10.36890/iejg.573919}, title = {Harmonic Aspects in an \$\\eta\$-Ricci Soliton}, key = {cite}, author = {BLAGA, Adara-monica} }
APA BLAGA, A . (2020). Harmonic Aspects in an $\eta$-Ricci Soliton. International Electronic Journal of Geometry , 13 (1) , 41-49 . DOI: 10.36890/iejg.573919
MLA BLAGA, A . "Harmonic Aspects in an $\eta$-Ricci Soliton". International Electronic Journal of Geometry 13 (2020 ): 41-49 <https://dergipark.org.tr/en/pub/iejg/issue/51297/573919>
Chicago BLAGA, A . "Harmonic Aspects in an $\eta$-Ricci Soliton". International Electronic Journal of Geometry 13 (2020 ): 41-49
RIS TY - JOUR T1 - Harmonic Aspects in an $\eta$-Ricci Soliton AU - Adara-monica BLAGA Y1 - 2020 PY - 2020 N1 - doi: 10.36890/iejg.573919 DO - 10.36890/iejg.573919 T2 - International Electronic Journal of Geometry JF - Journal JO - JOR SP - 41 EP - 49 VL - 13 IS - 1 SN - -1307-5624 M3 - doi: 10.36890/iejg.573919 UR - https://doi.org/10.36890/iejg.573919 Y2 - 2019 ER -
EndNote %0 International Electronic Journal of Geometry Harmonic Aspects in an $\eta$-Ricci Soliton %A Adara-monica BLAGA %T Harmonic Aspects in an $\eta$-Ricci Soliton %D 2020 %J International Electronic Journal of Geometry %P -1307-5624 %V 13 %N 1 %R doi: 10.36890/iejg.573919 %U 10.36890/iejg.573919
ISNAD BLAGA, Adara-monica . "Harmonic Aspects in an $\eta$-Ricci Soliton". International Electronic Journal of Geometry 13 / 1 (January 2020): 41-49 . https://doi.org/10.36890/iejg.573919
AMA BLAGA A . Harmonic Aspects in an $\eta$-Ricci Soliton. Int. Electron. J. Geom.. 2020; 13(1): 41-49.
Vancouver BLAGA A . Harmonic Aspects in an $\eta$-Ricci Soliton. International Electronic Journal of Geometry. 2020; 13(1): 49-41.