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Dergiler / International Electronic Journal of Geometry / 2020 / Cilt: 13 - Sayı: 1

Harmonic Aspects in an -Ricci Soliton

Adara M. Blaga
Sayfa
41–49
Yayın Tarihi
2022-10-18
DOI
—
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

In particular, we apply these results to a perfectfluid spacetime and using Bochner-Weitzenböck techniques, we formulate some more conclusionsfor gradient solitons and deduce topological properties of the manifold and its universal covering.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:We characterize -Ricci solitons (g; ; ; ) in some special cases when the 1-form , which is theg-dual of , is a harmonic or a Schrödinger-Ricci harmonic form.
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Temel Bulgular & Veri:We also provide necessary andsufficient conditions for to be a solution of the Schrödinger-Ricci equation and point out therelation between the three notions in our context.
💡
Sonuç & Katkı:In particular, we apply these results to a perfectfluid spacetime and using Bochner-Weitzenböck techniques, we formulate some more conclusionsfor gradient solitons and deduce topological properties of the manifold and its universal covering.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

We characterize -Ricci solitons (g; ; ; ) in some special cases when the 1-form , which is theg-dual of , is a harmonic or a Schrödinger-Ricci harmonic form. We also provide necessary andsufficient conditions for to be a solution of the Schrödinger-Ricci equation and point out therelation between the three notions in our context. In particular, we apply these results to a perfectfluid spacetime and using Bochner-Weitzenböck techniques, we formulate some more conclusionsfor gradient solitons and deduce topological properties of the manifold and its universal covering.

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Bu Makaleye Atıf Yap

Blaga, A. M. (2022). Harmonic Aspects in an -Ricci Soliton. International Electronic Journal of Geometry, Cilt: 13 - Sayı: 1, 41–49. https://ajindex.com/articles/539600

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Kaynakça (21)

  1. Blaga, A. M.: A note on almost -Ricci solitons in Euclidean hypersurfaces. Serdica Math. J. 43 (3-4), 361-368 (2017)
  2. Blaga, A. M.: A note on warped product almost quasi-Yamabe solitons. Filomat 33 (7), 2009-2016 (2019)
  3. Blaga, A. M.: Almost -Ricci solitons in (LCS)n-manifolds. Bull. Belg. Math. Soc. Simon Stevin 25 (5), 641-653 (2018)
  4. Blaga, A. M.: -Ricci solitons on Lorentzian para-Sasakian manifolds. Filomat 30 (2), 489-496 (2016)
  5. Blaga, A. M.: -Ricci solitons on para-Kenmotsu manifolds. Balkan J. Geom. Appl. 20 (1), 1-13 (2015)
  6. Blaga, A. M.: Last multipliers on -Ricci solitons. Matematichki Bilten 42 (2), 85-90 (2018)
  7. Blaga, A. M.: On gradient -Einstein solitons. Kragujevak J. Math. 42 (2), 229-237 (2018)
  8. Blaga, A. M.: On harmonicity and Miao-Tam critical metrics in a perfect fluid spacetime. To appear in Bol. Soc. Mat. Mexicana
  9. Blaga, A. M.: On solitons in statistical geometry. Int. J. Appl. Math. Stat. 58 (4), (2019)
  10. Blaga, A. M.: On warped product gradient -Ricci solitons. Filomat 31 (18), 5791-5801 (2017)
  11. Blaga, A. M.: Remarks on almost -solitons. Matematicki Vesnik 71 (3), 244-249 (2019)
  12. Blaga, A. M.: Solitons and geometrical structures in a perfect fluid spacetime. To appear in Rocky Mountain J. Math
  13. Blaga, A. M.: Solutions of some types of soliton equations in R3. Filomat 33 (4), 1159-1162 (2019)
  14. Blaga, A. M.: Some geometrical aspects of Einstein, Ricci and Yamabe solitons. J. Geom. Sym. Phys. 52, 17-26 (2019)
  15. Blaga, A. M., Baishya, K. K., Sarkar, N.: Ricci solitons in a generalized weakly (Ricci) symmetric D-homothetically deformed Kenmotsu manifold. Ann. Univ. Paedagog. Crac. Stud. Math. 18, 123-136 (2019)
  16. Blaga, A. M., Crasmareanu, M. C.: Inequalities for gradient Einstein and Ricci solitons. To appear in Facta Univ. Math. Inform
  17. Blaga, A. M., Crasmareanu, M. C.: Torse-forming -Ricci solitons in almost paracontact -Einstein geometry. Filomat 31 (2), 499-504 (2017)
  18. Blaga, A. M., Perkta¸s, S. Y.: Remarks on almost -Ricci solitons in "-para Sasakian manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 68 (2), 1621-1628 (2019)
  19. Blaga, A. M., Perkta¸s, S. Y., Acet, B. E., Erdogan, F. E.: -Ricci solitons in "-almost paracontact metric manifolds. Glasnik Matematicki 53 (1), 377-410 (2018)
  20. Catino, G.: A note on four-dimensional (anti-)self-dual quasi-Einstein manifolds. Differential Geom. Appl. 30, 660-664 (2012)
  21. C˘alin, C., Crasmar