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Conformal-twisted product semi-slant submanifolds in globally conformal Kaehler manifolds

Yıl 2021, Cilt: 50 Sayı: 4, 1028 - 1046, 06.08.2021
https://doi.org/10.15672/hujms.801651

Öz

We introduce the notion of conformal-twisted product submanifolds of the form $_fM^{T}\times_{b}M^{\theta}$ and $_fM^{\theta}\times_{b}M^{T}$, where $M^T$ is a holomorphic submanifold and $M^\theta$ is a proper slant submanifold of $M$ in a globally conformal Kaehler manifold and $f$ and $b$ are conformal factor and twisting function, respectively. We give necessary and sufficient conditions for proper semi-slant submanifold to be a locally conformal-twisted product for such submanifolds of the form $_fM^{T}\times_{b}M^{\theta}$ and $_fM^{\theta}\times_{b}M^{T}$. We establish a general inequality for the squared norm of second fundamental form of these types of submanifolds.

Destekleyen Kurum

TUBITAK

Proje Numarası

119F179

Kaynakça

  • [1] A. Bejancu, CR-Submanifolds of Kaehler manifold, Proc. Amer. Math. Soc. 69, 135- 142, 1978.
  • [2] A. Bejancu , Semi-invariant submanifolds of locally product Riemannian manifolds, An. Univ. West. Timis. Ser. Mat.-Inform. 22, 1984.
  • [3] R.L. Bishop and B. O’Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc. 1 (145), 1–49, 1969.
  • [4] V. Bonanzinga and K. Matsumoto, Twisted product CR-submanifolds in a locally conformal Kaehler space forms, Filomat, 34 (6), 1915–1925, 2020.
  • [5] B.Y. Chen, Geometry of submanifolds and its applications, Science University of Tokyo, 1981.
  • [6] B.Y. Chen, Geometry of slant submanifolds, Katholieke Universiteit, Leuven, Leuven 1990.
  • [7] B.Y. Chen, Geometry of warped product CR-submanifolds in Kaehler manifolds, Monatsh. Math. 133, 177–195, 2001.
  • [8] B.Y. Chen, Differential geometry of warped product manifolds and submanifolds, World Scientific, 2017.
  • [9] B.Y. Chen, F. Alghamdi and S. Uddin, Geometry of pointwise semi-slant warped products in locally conformal Kaehler manifolds, arXiv:2011.03997, 2020.
  • [10] S. Dragomir and L. Ornea, Locally conformal Kähler geometry, Progress in Mathematicsi 155, Birkhäuser, Boston Inc: Boston, MA, 1998.
  • [11] M. Gutierrez and B. Olea, Semi-Riemannian manifolds with a doubly warped structures, Rev. Mat. Iberoam. 28 (1), 1–24, 2012.
  • [12] M.A. Lone, A lower bound of normalized scalar curvature for the submanifolds of locally conformal Kaehler space form using Casorati curvatures, Filomat, 31 (15), 4925–4932, 2017.
  • [13] K. Matsumoto, Warped product semi-slant submanifolds in locally conformal Kaehler manifolds, Proc. Int. Geom. Cent. 10 (2), 8–23, 2017.
  • [14] K. Matsumoto, Warped product semi-slant submanifolds in locally conformal Kaehler manifolds II, Proc. Int. Geom. Cent. 11 (3), 27–44, 2018.
  • [15] M.I. Munteanu, Doubly warped product CR-submanifolds in locally conformal Kähler manifolds, Monatsh. Math. 150, 333–342, 2007.
  • [16] M.I. Munteanu, A note on doubly warped product contact CR-submanifolds in trans- Sasakian manifolds, Acta Math. Hungar. 116 (1-2), 121–126, 2007.
  • [17] N. Papaghiuc, Semi-slant submanifolds of a Kählerian manifold, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 40, 55–61, 1994.
  • [18] R. Ponge and H. Reckziegel, Twisted products pseudo- Riemannian geometry, Geom. Dedicata, 48, 15–25, 1993.
  • [19] B. Şahin, Nonexistence of warped product semi-slant submanifolds of Kaehler manifolds, Geom. Dedicata, 117, 195–202, 2005.
  • [20] B. Şahin, Notes on doubly warped and doubly twisted product CR-submanifolds of Kaehler manifolds, Mat. Vesnik, 59, 205–210, 2007.
  • [21] B. Şahin, Warped product semi-slant submanifolds of a locally product Riemannian manifold, Studia Sci. Math. Hungar. 46 (2), 169–184, 2009.
  • [22] H.M. Taştan and S. Gerdan, Doubly twisted product semi-invariant submanifolds of a locally product Riemannian manifold, Mathematical Advances in Pure and Applied Sciences, 1 (1), 23–26, 2018.
  • [23] H.M. Taştan and M.M. Tripathi, Semi-slant submanifolds of a locally conformal Kaehler manifold, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) Mathematics Tomul LXII, 1 (2), 337–347, 2016.
  • [24] S. Uddin, On doubly warped and doubly twisted product submanifolds, Int. Electron. J. Geom. 3 (1), 35–39, 2010.
  • [25] B. Ünal, Doubly warped products, Differential Geom. Appl. 15, 253–263, 2001.
  • [26] I. Vaisman, On locally and globally conformal Kähler manifolds, Trans. Amer. Math. Soc. 262 (2), 533–542, 1980.
  • [27] G.E. Vilcu, Ruled CR-submanifolds of locally conformal Kähler manifolds, J. Geom. Phys. 62 (6), 1366–1372, 2012.
  • [28] G.E. Vilcu, Horizontally conformal submersions from CR-submanifolds of locally conformal Kaehler manifolds, Mediterr. J. Math. 17 (26), 2020.
  • [29] K. Yano and M. Kon, Structures on Manifolds, World Scientific, Singapore, 1984.
Yıl 2021, Cilt: 50 Sayı: 4, 1028 - 1046, 06.08.2021
https://doi.org/10.15672/hujms.801651

Öz

Proje Numarası

119F179

Kaynakça

  • [1] A. Bejancu, CR-Submanifolds of Kaehler manifold, Proc. Amer. Math. Soc. 69, 135- 142, 1978.
  • [2] A. Bejancu , Semi-invariant submanifolds of locally product Riemannian manifolds, An. Univ. West. Timis. Ser. Mat.-Inform. 22, 1984.
  • [3] R.L. Bishop and B. O’Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc. 1 (145), 1–49, 1969.
  • [4] V. Bonanzinga and K. Matsumoto, Twisted product CR-submanifolds in a locally conformal Kaehler space forms, Filomat, 34 (6), 1915–1925, 2020.
  • [5] B.Y. Chen, Geometry of submanifolds and its applications, Science University of Tokyo, 1981.
  • [6] B.Y. Chen, Geometry of slant submanifolds, Katholieke Universiteit, Leuven, Leuven 1990.
  • [7] B.Y. Chen, Geometry of warped product CR-submanifolds in Kaehler manifolds, Monatsh. Math. 133, 177–195, 2001.
  • [8] B.Y. Chen, Differential geometry of warped product manifolds and submanifolds, World Scientific, 2017.
  • [9] B.Y. Chen, F. Alghamdi and S. Uddin, Geometry of pointwise semi-slant warped products in locally conformal Kaehler manifolds, arXiv:2011.03997, 2020.
  • [10] S. Dragomir and L. Ornea, Locally conformal Kähler geometry, Progress in Mathematicsi 155, Birkhäuser, Boston Inc: Boston, MA, 1998.
  • [11] M. Gutierrez and B. Olea, Semi-Riemannian manifolds with a doubly warped structures, Rev. Mat. Iberoam. 28 (1), 1–24, 2012.
  • [12] M.A. Lone, A lower bound of normalized scalar curvature for the submanifolds of locally conformal Kaehler space form using Casorati curvatures, Filomat, 31 (15), 4925–4932, 2017.
  • [13] K. Matsumoto, Warped product semi-slant submanifolds in locally conformal Kaehler manifolds, Proc. Int. Geom. Cent. 10 (2), 8–23, 2017.
  • [14] K. Matsumoto, Warped product semi-slant submanifolds in locally conformal Kaehler manifolds II, Proc. Int. Geom. Cent. 11 (3), 27–44, 2018.
  • [15] M.I. Munteanu, Doubly warped product CR-submanifolds in locally conformal Kähler manifolds, Monatsh. Math. 150, 333–342, 2007.
  • [16] M.I. Munteanu, A note on doubly warped product contact CR-submanifolds in trans- Sasakian manifolds, Acta Math. Hungar. 116 (1-2), 121–126, 2007.
  • [17] N. Papaghiuc, Semi-slant submanifolds of a Kählerian manifold, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 40, 55–61, 1994.
  • [18] R. Ponge and H. Reckziegel, Twisted products pseudo- Riemannian geometry, Geom. Dedicata, 48, 15–25, 1993.
  • [19] B. Şahin, Nonexistence of warped product semi-slant submanifolds of Kaehler manifolds, Geom. Dedicata, 117, 195–202, 2005.
  • [20] B. Şahin, Notes on doubly warped and doubly twisted product CR-submanifolds of Kaehler manifolds, Mat. Vesnik, 59, 205–210, 2007.
  • [21] B. Şahin, Warped product semi-slant submanifolds of a locally product Riemannian manifold, Studia Sci. Math. Hungar. 46 (2), 169–184, 2009.
  • [22] H.M. Taştan and S. Gerdan, Doubly twisted product semi-invariant submanifolds of a locally product Riemannian manifold, Mathematical Advances in Pure and Applied Sciences, 1 (1), 23–26, 2018.
  • [23] H.M. Taştan and M.M. Tripathi, Semi-slant submanifolds of a locally conformal Kaehler manifold, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) Mathematics Tomul LXII, 1 (2), 337–347, 2016.
  • [24] S. Uddin, On doubly warped and doubly twisted product submanifolds, Int. Electron. J. Geom. 3 (1), 35–39, 2010.
  • [25] B. Ünal, Doubly warped products, Differential Geom. Appl. 15, 253–263, 2001.
  • [26] I. Vaisman, On locally and globally conformal Kähler manifolds, Trans. Amer. Math. Soc. 262 (2), 533–542, 1980.
  • [27] G.E. Vilcu, Ruled CR-submanifolds of locally conformal Kähler manifolds, J. Geom. Phys. 62 (6), 1366–1372, 2012.
  • [28] G.E. Vilcu, Horizontally conformal submersions from CR-submanifolds of locally conformal Kaehler manifolds, Mediterr. J. Math. 17 (26), 2020.
  • [29] K. Yano and M. Kon, Structures on Manifolds, World Scientific, Singapore, 1984.
Toplam 29 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Sibel Gerdan Aydın 0000-0001-5278-6066

Hakan Mete Taştan 0000-0002-0773-9305

Proje Numarası 119F179
Yayımlanma Tarihi 6 Ağustos 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 50 Sayı: 4

Kaynak Göster

APA Gerdan Aydın, S., & Taştan, H. M. (2021). Conformal-twisted product semi-slant submanifolds in globally conformal Kaehler manifolds. Hacettepe Journal of Mathematics and Statistics, 50(4), 1028-1046. https://doi.org/10.15672/hujms.801651
AMA Gerdan Aydın S, Taştan HM. Conformal-twisted product semi-slant submanifolds in globally conformal Kaehler manifolds. Hacettepe Journal of Mathematics and Statistics. Ağustos 2021;50(4):1028-1046. doi:10.15672/hujms.801651
Chicago Gerdan Aydın, Sibel, ve Hakan Mete Taştan. “Conformal-Twisted Product Semi-Slant Submanifolds in Globally Conformal Kaehler Manifolds”. Hacettepe Journal of Mathematics and Statistics 50, sy. 4 (Ağustos 2021): 1028-46. https://doi.org/10.15672/hujms.801651.
EndNote Gerdan Aydın S, Taştan HM (01 Ağustos 2021) Conformal-twisted product semi-slant submanifolds in globally conformal Kaehler manifolds. Hacettepe Journal of Mathematics and Statistics 50 4 1028–1046.
IEEE S. Gerdan Aydın ve H. M. Taştan, “Conformal-twisted product semi-slant submanifolds in globally conformal Kaehler manifolds”, Hacettepe Journal of Mathematics and Statistics, c. 50, sy. 4, ss. 1028–1046, 2021, doi: 10.15672/hujms.801651.
ISNAD Gerdan Aydın, Sibel - Taştan, Hakan Mete. “Conformal-Twisted Product Semi-Slant Submanifolds in Globally Conformal Kaehler Manifolds”. Hacettepe Journal of Mathematics and Statistics 50/4 (Ağustos 2021), 1028-1046. https://doi.org/10.15672/hujms.801651.
JAMA Gerdan Aydın S, Taştan HM. Conformal-twisted product semi-slant submanifolds in globally conformal Kaehler manifolds. Hacettepe Journal of Mathematics and Statistics. 2021;50:1028–1046.
MLA Gerdan Aydın, Sibel ve Hakan Mete Taştan. “Conformal-Twisted Product Semi-Slant Submanifolds in Globally Conformal Kaehler Manifolds”. Hacettepe Journal of Mathematics and Statistics, c. 50, sy. 4, 2021, ss. 1028-46, doi:10.15672/hujms.801651.
Vancouver Gerdan Aydın S, Taştan HM. Conformal-twisted product semi-slant submanifolds in globally conformal Kaehler manifolds. Hacettepe Journal of Mathematics and Statistics. 2021;50(4):1028-46.