Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2024, Cilt: 17 Sayı: 1, 267 - 276, 23.04.2024

Milos B Djoric Mirjana Djoric

https://doi.org/10.36890/iejg.1454012

Öz

Kaynakça

  • [1] Bejancu, A.: CR-submanifolds of a Kähler manifold I. Proc. Amer. Math. Soc. 69, 135-142 (1978).
  • [2] Chen, B.-Y., Deshmukh, S.: Yamabe and quasi-Yamabe solitons on Euclidean submanifolds. Mediterr. J. Math. 15 (194), (2018).
  • [3] Chen, B.-Y., Djoric, M. B., Djoric, M.: Quasi-Yamabe and Yamabe solitons on hypersurfaces of nearly Kähler manifolds. Mediterr. J. Math. 21 (10), (2024).
  • [4] Cho, J. T., Kimura, M.: Ricci solitons and real hypersurfaces in a complex space form. Tohoku Math. J. 61 (2), 205-212 (2009).
  • [5] Cho, J. T., Kimura, M.: Ricci solitons of compact real hypersurfaces in Kähler manifolds. Math. Nachr. 284 (11-12), 1385-1393 (2011).
  • [6] Djoric, M., Okumura, M.: Certain CR submanifolds of maximal CR dimension of complex space forms. Differential Geom. Appl. 26, 208-217 (2008).
  • [7] Djoric, M., Okumura, M.: Scalar curvature of CR submanifolds of maximal CR dimension of complex projective space. Monatsh. Math. 154, 11-17 (2008).
  • [8] Djoric, M., Okumura, M.: CR submanifolds of complex projective space. Developments in Mathematics. 19 Springer, New York (2009).
  • [9] Hamilton, R. S.: The Ricci flow on surfaces. Math. Gen. Relativ. (Santa Cruz, CA, 1986), Contemp. Math. 71 Amer. Math. Soc. 237-262 (1988).
  • [10] Huang, G., Li, H.: On a classification of the quasi Yamabe gradient solitons. Methods Appl. Anal. 21 (3), 379-389 (2014).
  • [11] Kawamoto, S.: Codimension reduction for real submanifolds of complex hyperbolic space. Revista Mathematica de la Universidad Complutense de Madrid 7, 119-128 (1994).
  • [12] Leandro, B., Pina, H.: Generalized quasi Yamabe gradient solitons. J. Diff. Geom. Appl. 49, 167-175 (2016).
  • [13] Lee, J. M., Parker, T. H.: The Yamabe problem, Bull of Amer. Math. Soc. 17 (1), 37-91 (1987).
  • [14] Montiel, S., Romero, A.: On some real hypersurfaces of a complex hyperbolic space. Geom. Dedicata 20, 245-261 (1986).
  • [15] Niebergall, R., Ryan, P. J.: Real hypersurfaces in complex space forms. In: Tight and taut submanifolds. (eds. T. E. Cecil and S.-S. Chern) Math. Sci. Res. Inst. Publ. 32 Cambridge University Press, Cambridge 233-305 (1997).
  • [16] Okumura, M.: On some real hypersurfaces of a complex projective space. Trans. Amer. Math. Soc. 212, 355-364 (1975).
  • [17] Okumura, M.: Codimension reduction problem for real submanifolds of complex projective space. Colloq. Math. Soc. János Bolyai 56, 574-585 (1989).

Quasi Yamabe Solitons on CR Submanifolds of Maximal CR Dimension in Kähler Manifolds

Yıl 2024, Cilt: 17 Sayı: 1, 267 - 276, 23.04.2024

Milos B Djoric Mirjana Djoric

https://doi.org/10.36890/iejg.1454012

Öz

In this paper we give necessary and sufficient conditions for a CR submanifold of maximal CR
dimension in arbitrary Kähler manifold to admit (quasi-)Yamabe structure, with naturally chosen
soliton vector field. When the ambient manifold is a non-flat complex space form, we give a
complete classification of such solitons, under certain conditions.

Anahtar Kelimeler

Yamabe soliton quasi Yamabe soliton complex space form CR submanifold of maximal CR dimension structure vector field constant scalar curvature

Kaynakça

  • [1] Bejancu, A.: CR-submanifolds of a Kähler manifold I. Proc. Amer. Math. Soc. 69, 135-142 (1978).
  • [2] Chen, B.-Y., Deshmukh, S.: Yamabe and quasi-Yamabe solitons on Euclidean submanifolds. Mediterr. J. Math. 15 (194), (2018).
  • [3] Chen, B.-Y., Djoric, M. B., Djoric, M.: Quasi-Yamabe and Yamabe solitons on hypersurfaces of nearly Kähler manifolds. Mediterr. J. Math. 21 (10), (2024).
  • [4] Cho, J. T., Kimura, M.: Ricci solitons and real hypersurfaces in a complex space form. Tohoku Math. J. 61 (2), 205-212 (2009).
  • [5] Cho, J. T., Kimura, M.: Ricci solitons of compact real hypersurfaces in Kähler manifolds. Math. Nachr. 284 (11-12), 1385-1393 (2011).
  • [6] Djoric, M., Okumura, M.: Certain CR submanifolds of maximal CR dimension of complex space forms. Differential Geom. Appl. 26, 208-217 (2008).
  • [7] Djoric, M., Okumura, M.: Scalar curvature of CR submanifolds of maximal CR dimension of complex projective space. Monatsh. Math. 154, 11-17 (2008).
  • [8] Djoric, M., Okumura, M.: CR submanifolds of complex projective space. Developments in Mathematics. 19 Springer, New York (2009).
  • [9] Hamilton, R. S.: The Ricci flow on surfaces. Math. Gen. Relativ. (Santa Cruz, CA, 1986), Contemp. Math. 71 Amer. Math. Soc. 237-262 (1988).
  • [10] Huang, G., Li, H.: On a classification of the quasi Yamabe gradient solitons. Methods Appl. Anal. 21 (3), 379-389 (2014).
  • [11] Kawamoto, S.: Codimension reduction for real submanifolds of complex hyperbolic space. Revista Mathematica de la Universidad Complutense de Madrid 7, 119-128 (1994).
  • [12] Leandro, B., Pina, H.: Generalized quasi Yamabe gradient solitons. J. Diff. Geom. Appl. 49, 167-175 (2016).
  • [13] Lee, J. M., Parker, T. H.: The Yamabe problem, Bull of Amer. Math. Soc. 17 (1), 37-91 (1987).
  • [14] Montiel, S., Romero, A.: On some real hypersurfaces of a complex hyperbolic space. Geom. Dedicata 20, 245-261 (1986).
  • [15] Niebergall, R., Ryan, P. J.: Real hypersurfaces in complex space forms. In: Tight and taut submanifolds. (eds. T. E. Cecil and S.-S. Chern) Math. Sci. Res. Inst. Publ. 32 Cambridge University Press, Cambridge 233-305 (1997).
  • [16] Okumura, M.: On some real hypersurfaces of a complex projective space. Trans. Amer. Math. Soc. 212, 355-364 (1975).
  • [17] Okumura, M.: Codimension reduction problem for real submanifolds of complex projective space. Colloq. Math. Soc. János Bolyai 56, 574-585 (1989).
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Cebirsel ve Diferansiyel Geometri
Bölüm Araştırma Makalesi
Yazarlar

Milos B Djoric 0000-0001-5462-5522

Mirjana Djoric 0000-0003-3915-2928

Erken Görünüm Tarihi 15 Nisan 2024
Yayımlanma Tarihi 23 Nisan 2024
Gönderilme Tarihi 17 Mart 2024
Kabul Tarihi 7 Nisan 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 17 Sayı: 1

Kaynak Göster

APA Djoric, M. B., & Djoric, M. (2024). Quasi Yamabe Solitons on CR Submanifolds of Maximal CR Dimension in Kähler Manifolds. International Electronic Journal of Geometry, 17(1), 267-276. https://doi.org/10.36890/iejg.1454012
AMA Djoric MB, Djoric M. Quasi Yamabe Solitons on CR Submanifolds of Maximal CR Dimension in Kähler Manifolds. Int. Electron. J. Geom. Nisan 2024;17(1):267-276. doi:10.36890/iejg.1454012
Chicago Djoric, Milos B, ve Mirjana Djoric. “Quasi Yamabe Solitons on CR Submanifolds of Maximal CR Dimension in Kähler Manifolds”. International Electronic Journal of Geometry 17, sy. 1 (Nisan 2024): 267-76. https://doi.org/10.36890/iejg.1454012.
EndNote Djoric MB, Djoric M (01 Nisan 2024) Quasi Yamabe Solitons on CR Submanifolds of Maximal CR Dimension in Kähler Manifolds. International Electronic Journal of Geometry 17 1 267–276.
IEEE M. B. Djoric ve M. Djoric, “Quasi Yamabe Solitons on CR Submanifolds of Maximal CR Dimension in Kähler Manifolds”, Int. Electron. J. Geom., c. 17, sy. 1, ss. 267–276, 2024, doi: 10.36890/iejg.1454012.
ISNAD Djoric, Milos B - Djoric, Mirjana. “Quasi Yamabe Solitons on CR Submanifolds of Maximal CR Dimension in Kähler Manifolds”. International Electronic Journal of Geometry 17/1 (Nisan 2024), 267-276. https://doi.org/10.36890/iejg.1454012.
JAMA Djoric MB, Djoric M. Quasi Yamabe Solitons on CR Submanifolds of Maximal CR Dimension in Kähler Manifolds. Int. Electron. J. Geom. 2024;17:267–276.
MLA Djoric, Milos B ve Mirjana Djoric. “Quasi Yamabe Solitons on CR Submanifolds of Maximal CR Dimension in Kähler Manifolds”. International Electronic Journal of Geometry, c. 17, sy. 1, 2024, ss. 267-76, doi:10.36890/iejg.1454012.
Vancouver Djoric MB, Djoric M. Quasi Yamabe Solitons on CR Submanifolds of Maximal CR Dimension in Kähler Manifolds. Int. Electron. J. Geom. 2024;17(1):267-76.
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