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Solitons on Nearly Cosymplectic Manifold Exhibitting Schouten Van Kampen Connection

Yıl 2024, , 220 - 228, 31.12.2024

Pushpa Bora , Jaya Upreti , Shankar Kumar

https://doi.org/10.33434/cams.1541298

Öz

The following research investigates various types of soliton of NC (Nearly Cosymplectic) manifolds with SVK (Schouten-van Kampen) connections, which are steady, shrinking, or expanding. Further, we investigate the geometric characteristics of Ricci solitons, Yamabe solitons, $\eta$-ricci soliton etc. We also study the curvature features of the SVK connection on an NC manifold. In addition, an example is developed to demonstrate the results.

Anahtar Kelimeler

Einstein manifold Nearly cosymplectic manifold Quasi Einstein manifold Ricci soliton Schouten van Kampen connection Yamabe soliton

Proje Numarası

DST/WISE-PhD/PM/2023/6(G)

Teşekkür

The author acknowledges the Department of Science & Technology, Government of India, for financial support vide reference no DST/WISE-PhD/PM/2023/6(Gunder 'WISE FELLOWSHIP for Ph.D.' to carry out this work.

Kaynakça

  • [1] A. Bejancu, H. R. Farran, Foliations and Geometric Structures, Springer Science and Business Media, (580) (2006).
  • [2] A. Dündar, N. Aktan, Some results on nearly cosymplectic manifolds, Univ. J. Math. Appl., 2(4) (2019), 218-223.
  • [3] R. Kundu, A. Das, A. Biswas, Conformal Ricci soliton in Sasakian manifolds admitting general connection, J. Hyperstruct., 13(1) (2024), 46-61.
  • [4] S. Sundriyal, J. Upreti, Solitons on Para-Sasakian manifold with respect to the Schouten-Van Kampen connection, Ganita Vol., 73(1) (2023), 25-33.
  • [5] A. Yıldız, f-Kenmotsu manifolds with the Schouten-Van Kampen connection, Publications de l’Institut Mathematique, 102(116) (2017), 93-105.
  • [6] G. Ghosh, On Schouten-Van Kampen connection in Sasakian manifolds, Boletim da Sociedade Paranaense de Mathematica, 36 (2018), 171-182.
  • [7] M. Altunbaş, Some characterizations of hyperbolic Ricci solitons on nearly cosymplectic manifolds with respect to the Tanaka-Webster connection, Istanbul J. Math., 2(1) (2024), 28-32.
  • [8] D. Blair, Almost contact manifolds with Killing structure tensors, Pacific J. Math., 39(2) (1971), 285-292.
  • [9] J. T. Cho, M. Kimura, Ricci solitons and real hypersurfaces in a complex space form, Tˆohoku Math. J., Second Series, 61(2) (2009), 205-212.
  • [10] R. S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geometry, 17(2) (1982), 255-306.
  • [11] R. S. Hamilton, The Ricci flow on surfaces, Contemp. Math., 71, (1988) 237-261.
  • [12] G. Perelman, The entropy formula for the Ricci flow and its geometric applications, arXiv preprint math/0211159 (2002).
  • [13] G. Perelman, Ricci flow with surgery on three-manifolds, arXiv preprint math/0303109 (2003).
  • [14] T. Ivey, Ricci solitons on compact three-manifolds, Differential Geom. Appl., 3(4) (1993), 301-307.
  • [15] K. De, U. C. De, Conharmonic curvature tensor on Kenmotsu manifolds, Bull. Transilv. Univ. Bras¸ov Ser. III. Math. Comput. Sci., 6(55) (2013), 9-22.
  • [16] A. De Nicola, G. Dileo, I. Yudin, On nearly Sasakian and nearly cosymplectic manifolds, Ann. Mat. Pura Appl., (197) (2018), 127-138.
  • [17] A. F. Solovev, Curvature of a distribution, Mathematical Notes of the Academy of Sciences of the USSR 35 (1984), 61-68.
  • [18] A. F. Solovev, On the curvature of the connection induced on a hyperdistribution in a Riemannian space, Geom. Sb, 19 (1978), 12-23.
  • [19] M. C. Chaki, R. K. Maity, On quasi Einstein manifolds, Publ. Math. Debrecen, 57 (2000), 297-306.
  • [20] G. P. Pokhariyal, R. S. Mishra, Curvature tensors and their relativistic significance (II), The Yokohama Math. J., 19(2) (1971), 97-103.

Yıl 2024, , 220 - 228, 31.12.2024

Pushpa Bora , Jaya Upreti , Shankar Kumar

https://doi.org/10.33434/cams.1541298

Öz

Proje Numarası

DST/WISE-PhD/PM/2023/6(G)

Kaynakça

  • [1] A. Bejancu, H. R. Farran, Foliations and Geometric Structures, Springer Science and Business Media, (580) (2006).
  • [2] A. Dündar, N. Aktan, Some results on nearly cosymplectic manifolds, Univ. J. Math. Appl., 2(4) (2019), 218-223.
  • [3] R. Kundu, A. Das, A. Biswas, Conformal Ricci soliton in Sasakian manifolds admitting general connection, J. Hyperstruct., 13(1) (2024), 46-61.
  • [4] S. Sundriyal, J. Upreti, Solitons on Para-Sasakian manifold with respect to the Schouten-Van Kampen connection, Ganita Vol., 73(1) (2023), 25-33.
  • [5] A. Yıldız, f-Kenmotsu manifolds with the Schouten-Van Kampen connection, Publications de l’Institut Mathematique, 102(116) (2017), 93-105.
  • [6] G. Ghosh, On Schouten-Van Kampen connection in Sasakian manifolds, Boletim da Sociedade Paranaense de Mathematica, 36 (2018), 171-182.
  • [7] M. Altunbaş, Some characterizations of hyperbolic Ricci solitons on nearly cosymplectic manifolds with respect to the Tanaka-Webster connection, Istanbul J. Math., 2(1) (2024), 28-32.
  • [8] D. Blair, Almost contact manifolds with Killing structure tensors, Pacific J. Math., 39(2) (1971), 285-292.
  • [9] J. T. Cho, M. Kimura, Ricci solitons and real hypersurfaces in a complex space form, Tˆohoku Math. J., Second Series, 61(2) (2009), 205-212.
  • [10] R. S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geometry, 17(2) (1982), 255-306.
  • [11] R. S. Hamilton, The Ricci flow on surfaces, Contemp. Math., 71, (1988) 237-261.
  • [12] G. Perelman, The entropy formula for the Ricci flow and its geometric applications, arXiv preprint math/0211159 (2002).
  • [13] G. Perelman, Ricci flow with surgery on three-manifolds, arXiv preprint math/0303109 (2003).
  • [14] T. Ivey, Ricci solitons on compact three-manifolds, Differential Geom. Appl., 3(4) (1993), 301-307.
  • [15] K. De, U. C. De, Conharmonic curvature tensor on Kenmotsu manifolds, Bull. Transilv. Univ. Bras¸ov Ser. III. Math. Comput. Sci., 6(55) (2013), 9-22.
  • [16] A. De Nicola, G. Dileo, I. Yudin, On nearly Sasakian and nearly cosymplectic manifolds, Ann. Mat. Pura Appl., (197) (2018), 127-138.
  • [17] A. F. Solovev, Curvature of a distribution, Mathematical Notes of the Academy of Sciences of the USSR 35 (1984), 61-68.
  • [18] A. F. Solovev, On the curvature of the connection induced on a hyperdistribution in a Riemannian space, Geom. Sb, 19 (1978), 12-23.
  • [19] M. C. Chaki, R. K. Maity, On quasi Einstein manifolds, Publ. Math. Debrecen, 57 (2000), 297-306.
  • [20] G. P. Pokhariyal, R. S. Mishra, Curvature tensors and their relativistic significance (II), The Yokohama Math. J., 19(2) (1971), 97-103.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Cebirsel ve Diferansiyel Geometri
Bölüm Makaleler
Yazarlar

Pushpa Bora 0009-0005-4283-7014

Jaya Upreti 0000-0001-8615-1819

Shankar Kumar 0000-0002-6094-5626

Proje Numarası DST/WISE-PhD/PM/2023/6(G)
Erken Görünüm Tarihi 31 Aralık 2024
Yayımlanma Tarihi 31 Aralık 2024
Gönderilme Tarihi 31 Ağustos 2024
Kabul Tarihi 31 Aralık 2024
Yayımlandığı Sayı Yıl 2024

Kaynak Göster

APA Bora, P., Upreti, J., & Kumar, S. (2024). Solitons on Nearly Cosymplectic Manifold Exhibitting Schouten Van Kampen Connection. Communications in Advanced Mathematical Sciences, 7(4), 220-228. https://doi.org/10.33434/cams.1541298
AMA Bora P, Upreti J, Kumar S. Solitons on Nearly Cosymplectic Manifold Exhibitting Schouten Van Kampen Connection. Communications in Advanced Mathematical Sciences. Aralık 2024;7(4):220-228. doi:10.33434/cams.1541298
Chicago Bora, Pushpa, Jaya Upreti, ve Shankar Kumar. “Solitons on Nearly Cosymplectic Manifold Exhibitting Schouten Van Kampen Connection”. Communications in Advanced Mathematical Sciences 7, sy. 4 (Aralık 2024): 220-28. https://doi.org/10.33434/cams.1541298.
EndNote Bora P, Upreti J, Kumar S (01 Aralık 2024) Solitons on Nearly Cosymplectic Manifold Exhibitting Schouten Van Kampen Connection. Communications in Advanced Mathematical Sciences 7 4 220–228.
IEEE P. Bora, J. Upreti, ve S. Kumar, “Solitons on Nearly Cosymplectic Manifold Exhibitting Schouten Van Kampen Connection”, Communications in Advanced Mathematical Sciences, c. 7, sy. 4, ss. 220–228, 2024, doi: 10.33434/cams.1541298.
ISNAD Bora, Pushpa vd. “Solitons on Nearly Cosymplectic Manifold Exhibitting Schouten Van Kampen Connection”. Communications in Advanced Mathematical Sciences 7/4 (Aralık 2024), 220-228. https://doi.org/10.33434/cams.1541298.
JAMA Bora P, Upreti J, Kumar S. Solitons on Nearly Cosymplectic Manifold Exhibitting Schouten Van Kampen Connection. Communications in Advanced Mathematical Sciences. 2024;7:220–228.
MLA Bora, Pushpa vd. “Solitons on Nearly Cosymplectic Manifold Exhibitting Schouten Van Kampen Connection”. Communications in Advanced Mathematical Sciences, c. 7, sy. 4, 2024, ss. 220-8, doi:10.33434/cams.1541298.
Vancouver Bora P, Upreti J, Kumar S. Solitons on Nearly Cosymplectic Manifold Exhibitting Schouten Van Kampen Connection. Communications in Advanced Mathematical Sciences. 2024;7(4):220-8.

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