Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2023, Cilt: 6 Sayı: 1, 35 - 41, 29.03.2023
https://doi.org/10.33401/fujma.1153224

Öz

Kaynakça

  • [1] S. Desmukh, F. Alsolamy, Conformal vector fields on a Riemannian manifold, Balkan J. Geom. Appl. 19 (2014), 86-93.
  • [2] M. Obata, Conformal transformations of Riemannian manifolds, J. Diff. Geom. 4 (1970), 311-333.
  • [3] S. Tanno, W. Weber, Closed conformal vector fields, J. Diff. Geom. 3 (1969), 361-366.
  • [4] R. Sharma, Holomorphically planar conformal vector fields on almost Hermitian manifolds, Contemp. Math. 337 (2003), 145-154.
  • [5] A. Ghosh, R. Sharma, Almost Hermitian manifolds admitting holomorphically planar conformal vector fields, J. Geom., 84 (2005), 45-54.
  • [6] A. Ghosh, Holomorphically planar conformal vector fields on contact metric manifolds, Acta Math. Hungar., 129 (2010), 357-367.
  • [7] B. Cappelletti-Montano, De Nicola, A.I. Yudin, A survey on cosymplectic geometry. Rev. Math. Phys., 25 (2013), 1343002.
  • [8] S.I. Goldberg, K. Yano, Integrability of almost cosymplectic structure. Pac. J. Math., 31 (1969), 373-382.
  • [9] H. Endo, Non-existence of almost cosymplectic manifolds satisfying a certain condition, Tensor (N.S.), 284(3) (2002), 272-289.
  • [10] K. Kenmotsu, A class of almost contact Riemannian manifolds. Tˆohoku Math. J., 24 (1972), 93-103.
  • [11] T.W. Kim, H.K. Pak, Canonical foliations of certain classes of almost contact metric structures, Acta Math. Sin. Eng. Ser., 21 (2005), 841–846.
  • [12] N. Aktan, H. O¨ ztu¨rk, C. Murathan, Almost a-cosymplectic (k;m;n)􀀀spaces, arXiv:1007.0527v1.
  • [13] S. Beyendi, G. Ayar, N. Aktan, On a type of a-cosymplectic manifolds, Commun. Fac. Sci. Univ. Ankara, Ser. A1, Math. Stat., 68 (2019), 852-861.
  • [14] S. Beyendi, M. Yıldırım, On generalized weakly symmetric a-cosymplectic manifolds, Hacet. J. Math. Stat., 50(6) (2021), 1745-1755.
  • [15] M. Yıldırım, S. Beyendi, On almost generalized weakly symmetric a-cosymplectic manifolds, Univers. J. Math. Appl., 3(4) (2020), 156-159, doi:10.32323/ujma.730960.
  • [16] H. İ. Yoldai, Some results on cosymplectic manifolds admitting certain vector fields, JGSP, 60 (2021), 83-94.
  • [17] H. İ. Yoldaş, Ş. Eken Meriç, E. Yaşar, Some characterizations of a-cosymplectic manifolds admitting Yamabe solitons, Palestine Journal of Math., 10 (2021), 234-241.
  • [18] M. Obata, Certain conditions for a Riemannian manifold to be isometric with a sphere, J. Math. Soc. Japan., 14 (1962), 333-340.

Holomorphically Planar Conformal Vector Field On Almost $\alpha $-Cosymplectic $(\kappa ,\mu )-$ Spaces

Yıl 2023, Cilt: 6 Sayı: 1, 35 - 41, 29.03.2023
https://doi.org/10.33401/fujma.1153224

Öz

The aim of the present paper is to study holomorphically planar conformal vector (HPCV) fields on almost αα−cosymplectic (κ,μ)(κ,μ)−spaces. This is done assuming various conditions such as i) UU is pointwise collinear with ξξ ( in this case, the integral manifold of the distribution DD is totally geodesic, or totally umbilical), ii) MM has a constant ξξ−sectional curvature (under this condition the integral manifold of the distribution DD is totally geodesic (or totally umbilical) or the manifold is isometric to sphere S2n+1(c)S2n+1(c) of radius 1c1c), iii) MM an almost αα−cosymplectic (κ,μ)(κ,μ)−spaces ( in this case the manifold has constant curvature, or the integral manifold of the distribution DD is totally geodesic(or totally umbilical) or UU is an eigenvector of h).h).

Kaynakça

  • [1] S. Desmukh, F. Alsolamy, Conformal vector fields on a Riemannian manifold, Balkan J. Geom. Appl. 19 (2014), 86-93.
  • [2] M. Obata, Conformal transformations of Riemannian manifolds, J. Diff. Geom. 4 (1970), 311-333.
  • [3] S. Tanno, W. Weber, Closed conformal vector fields, J. Diff. Geom. 3 (1969), 361-366.
  • [4] R. Sharma, Holomorphically planar conformal vector fields on almost Hermitian manifolds, Contemp. Math. 337 (2003), 145-154.
  • [5] A. Ghosh, R. Sharma, Almost Hermitian manifolds admitting holomorphically planar conformal vector fields, J. Geom., 84 (2005), 45-54.
  • [6] A. Ghosh, Holomorphically planar conformal vector fields on contact metric manifolds, Acta Math. Hungar., 129 (2010), 357-367.
  • [7] B. Cappelletti-Montano, De Nicola, A.I. Yudin, A survey on cosymplectic geometry. Rev. Math. Phys., 25 (2013), 1343002.
  • [8] S.I. Goldberg, K. Yano, Integrability of almost cosymplectic structure. Pac. J. Math., 31 (1969), 373-382.
  • [9] H. Endo, Non-existence of almost cosymplectic manifolds satisfying a certain condition, Tensor (N.S.), 284(3) (2002), 272-289.
  • [10] K. Kenmotsu, A class of almost contact Riemannian manifolds. Tˆohoku Math. J., 24 (1972), 93-103.
  • [11] T.W. Kim, H.K. Pak, Canonical foliations of certain classes of almost contact metric structures, Acta Math. Sin. Eng. Ser., 21 (2005), 841–846.
  • [12] N. Aktan, H. O¨ ztu¨rk, C. Murathan, Almost a-cosymplectic (k;m;n)􀀀spaces, arXiv:1007.0527v1.
  • [13] S. Beyendi, G. Ayar, N. Aktan, On a type of a-cosymplectic manifolds, Commun. Fac. Sci. Univ. Ankara, Ser. A1, Math. Stat., 68 (2019), 852-861.
  • [14] S. Beyendi, M. Yıldırım, On generalized weakly symmetric a-cosymplectic manifolds, Hacet. J. Math. Stat., 50(6) (2021), 1745-1755.
  • [15] M. Yıldırım, S. Beyendi, On almost generalized weakly symmetric a-cosymplectic manifolds, Univers. J. Math. Appl., 3(4) (2020), 156-159, doi:10.32323/ujma.730960.
  • [16] H. İ. Yoldai, Some results on cosymplectic manifolds admitting certain vector fields, JGSP, 60 (2021), 83-94.
  • [17] H. İ. Yoldaş, Ş. Eken Meriç, E. Yaşar, Some characterizations of a-cosymplectic manifolds admitting Yamabe solitons, Palestine Journal of Math., 10 (2021), 234-241.
  • [18] M. Obata, Certain conditions for a Riemannian manifold to be isometric with a sphere, J. Math. Soc. Japan., 14 (1962), 333-340.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Mustafa Yıldırım 0000-0002-7885-1492

Nesip Aktan 0000-0002-6825-4563

Yayımlanma Tarihi 29 Mart 2023
Gönderilme Tarihi 2 Ağustos 2022
Kabul Tarihi 4 Kasım 2022
Yayımlandığı Sayı Yıl 2023 Cilt: 6 Sayı: 1

Kaynak Göster

APA Yıldırım, M., & Aktan, N. (2023). Holomorphically Planar Conformal Vector Field On Almost $\alpha $-Cosymplectic $(\kappa ,\mu )-$ Spaces. Fundamental Journal of Mathematics and Applications, 6(1), 35-41. https://doi.org/10.33401/fujma.1153224
AMA Yıldırım M, Aktan N. Holomorphically Planar Conformal Vector Field On Almost $\alpha $-Cosymplectic $(\kappa ,\mu )-$ Spaces. Fundam. J. Math. Appl. Mart 2023;6(1):35-41. doi:10.33401/fujma.1153224
Chicago Yıldırım, Mustafa, ve Nesip Aktan. “Holomorphically Planar Conformal Vector Field On Almost $\alpha $-Cosymplectic $(\kappa ,\mu )-$ Spaces”. Fundamental Journal of Mathematics and Applications 6, sy. 1 (Mart 2023): 35-41. https://doi.org/10.33401/fujma.1153224.
EndNote Yıldırım M, Aktan N (01 Mart 2023) Holomorphically Planar Conformal Vector Field On Almost $\alpha $-Cosymplectic $(\kappa ,\mu )-$ Spaces. Fundamental Journal of Mathematics and Applications 6 1 35–41.
IEEE M. Yıldırım ve N. Aktan, “Holomorphically Planar Conformal Vector Field On Almost $\alpha $-Cosymplectic $(\kappa ,\mu )-$ Spaces”, Fundam. J. Math. Appl., c. 6, sy. 1, ss. 35–41, 2023, doi: 10.33401/fujma.1153224.
ISNAD Yıldırım, Mustafa - Aktan, Nesip. “Holomorphically Planar Conformal Vector Field On Almost $\alpha $-Cosymplectic $(\kappa ,\mu )-$ Spaces”. Fundamental Journal of Mathematics and Applications 6/1 (Mart 2023), 35-41. https://doi.org/10.33401/fujma.1153224.
JAMA Yıldırım M, Aktan N. Holomorphically Planar Conformal Vector Field On Almost $\alpha $-Cosymplectic $(\kappa ,\mu )-$ Spaces. Fundam. J. Math. Appl. 2023;6:35–41.
MLA Yıldırım, Mustafa ve Nesip Aktan. “Holomorphically Planar Conformal Vector Field On Almost $\alpha $-Cosymplectic $(\kappa ,\mu )-$ Spaces”. Fundamental Journal of Mathematics and Applications, c. 6, sy. 1, 2023, ss. 35-41, doi:10.33401/fujma.1153224.
Vancouver Yıldırım M, Aktan N. Holomorphically Planar Conformal Vector Field On Almost $\alpha $-Cosymplectic $(\kappa ,\mu )-$ Spaces. Fundam. J. Math. Appl. 2023;6(1):35-41.

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