Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2023, Cilt: 16 Sayı: 1, 266 - 271, 30.04.2023
https://doi.org/10.36890/iejg.1286128

Öz

Kaynakça

  • [1] Barros, A. and Ribeiro, E.: Integral formulae on quasi-Einstein manifolds and applications, Glasg. Math. J. 54, 213-223 (2012).
  • [2] Barros, A. and Ribeiro, E.: Characterizations and integral formulae for generalized m-quasi-Einstein metrics, Bull. Braz. Math. Soc., New Series 45, 325-341 (2014).
  • [3] Case, J., Shu, Y. and Wei, G.: Rigidity of quasi-Einstein metrics, Diff. Geom. Appl. 29, 93-100 (2011).
  • [4] Catino, G.: Generalized quasi-Einstein manifolds with harmonic Weyl tensor, Math. Zeits. 271, 751-756 (2012).
  • [5] Ghosh, A. & Sharma, R.: Sasakian metric as a Ricci soliton and related results, Journal of Geometry and Physics 75, 1-6 (2014).
  • [6] He, C., Petersen, P. Wylie, W.: On the classification of warped product Einstein metrics, ArXiv Preprint ArXiv: 1010.5488, (2010).
  • [7] Pigola, S., Rigoli, M., Rimoldi, M. and Setti, A.G.: Ricci almost solitons, Ann.Della Scuola Norm. Sup. Di Pisa-Classe Di Sci. 10, 757-799 (2011).
  • [8] Sharma, R.: Some results on almost Ricci solitons and geodesic vector fields, Beitr. Alg. Geom. 59, 289-294 (2018).
  • [9] Tashiro, Y.: Complete Riemannian manifolds and some vector fields. Trans. Amer. Math. Soc. 117, 251-275 (1965).
  • [10] Yano, K.: Integral formulas in Riemannian geometry, Marcel Dekker, 1970.

Rigidity Results On Generalized m-Quasi Einstein Manifolds with Associated Affine Killing Vector Field.

Yıl 2023, Cilt: 16 Sayı: 1, 266 - 271, 30.04.2023
https://doi.org/10.36890/iejg.1286128

Öz

We study a non-trivial generalized $m$-quasi Einstein manifold $M$ with finite $m$ and associated divergence-free affine Killing vector field, and show that $M$ reduces to an $m$-quasi Einstein manifold. In addition, if $M$ is complete, then it splits as the product of a line and an $(n-1)$-dimensional negatively Einstein manifold. Finally, we show that the same result holds for a complete non-trivial $m$-quasi Einstein manifold $M$ with finite $m$ and associated affine Killing vector field.

Kaynakça

  • [1] Barros, A. and Ribeiro, E.: Integral formulae on quasi-Einstein manifolds and applications, Glasg. Math. J. 54, 213-223 (2012).
  • [2] Barros, A. and Ribeiro, E.: Characterizations and integral formulae for generalized m-quasi-Einstein metrics, Bull. Braz. Math. Soc., New Series 45, 325-341 (2014).
  • [3] Case, J., Shu, Y. and Wei, G.: Rigidity of quasi-Einstein metrics, Diff. Geom. Appl. 29, 93-100 (2011).
  • [4] Catino, G.: Generalized quasi-Einstein manifolds with harmonic Weyl tensor, Math. Zeits. 271, 751-756 (2012).
  • [5] Ghosh, A. & Sharma, R.: Sasakian metric as a Ricci soliton and related results, Journal of Geometry and Physics 75, 1-6 (2014).
  • [6] He, C., Petersen, P. Wylie, W.: On the classification of warped product Einstein metrics, ArXiv Preprint ArXiv: 1010.5488, (2010).
  • [7] Pigola, S., Rigoli, M., Rimoldi, M. and Setti, A.G.: Ricci almost solitons, Ann.Della Scuola Norm. Sup. Di Pisa-Classe Di Sci. 10, 757-799 (2011).
  • [8] Sharma, R.: Some results on almost Ricci solitons and geodesic vector fields, Beitr. Alg. Geom. 59, 289-294 (2018).
  • [9] Tashiro, Y.: Complete Riemannian manifolds and some vector fields. Trans. Amer. Math. Soc. 117, 251-275 (1965).
  • [10] Yano, K.: Integral formulas in Riemannian geometry, Marcel Dekker, 1970.
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Rahul Poddar 0000-0002-5671-2774

Balasubramanian Subramanian 0000-0001-8947-4840

R. Sharma 0000-0001-5026-8564

Yayımlanma Tarihi 30 Nisan 2023
Kabul Tarihi 20 Nisan 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 16 Sayı: 1

Kaynak Göster

APA Poddar, R., Subramanian, B., & Sharma, R. (2023). Rigidity Results On Generalized m-Quasi Einstein Manifolds with Associated Affine Killing Vector Field. International Electronic Journal of Geometry, 16(1), 266-271. https://doi.org/10.36890/iejg.1286128
AMA Poddar R, Subramanian B, Sharma R. Rigidity Results On Generalized m-Quasi Einstein Manifolds with Associated Affine Killing Vector Field. Int. Electron. J. Geom. Nisan 2023;16(1):266-271. doi:10.36890/iejg.1286128
Chicago Poddar, Rahul, Balasubramanian Subramanian, ve R. Sharma. “Rigidity Results On Generalized M-Quasi Einstein Manifolds With Associated Affine Killing Vector Field”. International Electronic Journal of Geometry 16, sy. 1 (Nisan 2023): 266-71. https://doi.org/10.36890/iejg.1286128.
EndNote Poddar R, Subramanian B, Sharma R (01 Nisan 2023) Rigidity Results On Generalized m-Quasi Einstein Manifolds with Associated Affine Killing Vector Field. International Electronic Journal of Geometry 16 1 266–271.
IEEE R. Poddar, B. Subramanian, ve R. Sharma, “Rigidity Results On Generalized m-Quasi Einstein Manifolds with Associated Affine Killing Vector Field”., Int. Electron. J. Geom., c. 16, sy. 1, ss. 266–271, 2023, doi: 10.36890/iejg.1286128.
ISNAD Poddar, Rahul vd. “Rigidity Results On Generalized M-Quasi Einstein Manifolds With Associated Affine Killing Vector Field”. International Electronic Journal of Geometry 16/1 (Nisan 2023), 266-271. https://doi.org/10.36890/iejg.1286128.
JAMA Poddar R, Subramanian B, Sharma R. Rigidity Results On Generalized m-Quasi Einstein Manifolds with Associated Affine Killing Vector Field. Int. Electron. J. Geom. 2023;16:266–271.
MLA Poddar, Rahul vd. “Rigidity Results On Generalized M-Quasi Einstein Manifolds With Associated Affine Killing Vector Field”. International Electronic Journal of Geometry, c. 16, sy. 1, 2023, ss. 266-71, doi:10.36890/iejg.1286128.
Vancouver Poddar R, Subramanian B, Sharma R. Rigidity Results On Generalized m-Quasi Einstein Manifolds with Associated Affine Killing Vector Field. Int. Electron. J. Geom. 2023;16(1):266-71.