An inequality for warped product submanifolds of a locally product Riemannian manifold

Falleh R. Al-solamy; Siraj Uddin

Araştırma Makalesi

An inequality for warped product submanifolds of a locally product Riemannian manifold

Yıl 2019, Cilt: 48 Sayı: 2, 351 - 358, 01.04.2019

Falleh R. Al-solamy Siraj Uddin

Öz

Recently, Sahin studied the warped product semi-slant submanifolds of locally product Riemannian manifolds. In this paper, we obtain some geometric properties of such submanifolds with an example. Also, we establish a sharp relationship between the squared norm of the second fundamental form and the warping function in terms of the slant angle. The equality case is also considered.

Anahtar Kelimeler

slant submanifolds, semi-slant submanifolds, mixed totally geodesic, warped product semi-slant submanifolds, locally product Riemannian manifolds

Kaynakça

M. Atceken, Warped product semi-slant submanifolds in locally Riemannian product manifolds, Bull. Austral. Math. Soc. 77, 177–186, 2008.
M. Atceken, Geometry of warped product semi-invariant submanifolds of a locally Riemannian product manifold, Serdica Math. J. 35, 273–286, 2009.
M. Atceken, Warped product semi-invariant submanifolds in locally decomposable Riemannian manifolds, Hacet. J. Math. Stat. 40, 401–407, 2011.
A. Bejancu, Semi-invariant submanifolds of locally Riemannian product manifolds, Ann. Univ. Timisoara S. Math. 22, 3–11, 1984.
R.L. Bishop and B. O’Neill, Manifolds of Negative curvature, Trans. Amer. Math. Soc. 145, 1–49, 1969.
B.Y. Chen, Slant immersions, Bull. Austral. Math. Soc. 41, 135–147, 1990.
H. Li and X. Li, Semi-slant submanifolds of locally product manifolds, Georgian Math. J. 12, 273–282, 2005.
K. Matsumoto, On submanifolds of locally product Riemannian manifolds, TRU Math. 18, 145–157, 1982.
N. Papaghiuc, Semi-slant submanifolds of Kaehlerian manifold, Ann. St. Univ. Iasi, 9, 55–61, 1994.
B. Sahin, Slant submanifolds of an almost product Riemannian manifold, J. Korean Math. Soc. 43, 717–732, 2006.
B. Sahin, Warped product semi-invariant submanifolds of locally product Riemannian manifolds, Bull. Math. Soc. Sci. Math. Roumanie Tome, 49 (97), 383–394, 2006.
B. Sahin, Warped product semi-slant submanifolds of a locally product Riemannian manifold, Studia Sci. Math. Hungar. 46, 169–184, 2009.
S. Uddin and F.R. Al-Solamy, Warped product pseudo-slant submanifolds of cosymplectic manifolds, An. Ştiinţ. Univ. Al. I. Cuza Iaşi Mat. (N.S.) Tomul LXII, (f. 2,3), 901–913, 2016.
S. Uddin and F.R. Al-Solamy, Warped product pseudo-slant immersions in Sasakian manifolds, Publ. Math. Debrecen, 91 (3-4), 331–348, 2017.
S. Uddin, A. Ali, N.M. Al-Asmari and W.A. Othman, Warped product pseudo-slant submanifolds in a locally product Riemannian manifold, Diff. Geometry Dyn. Syst. 18, 147–158, 2016.
S. Uddin, B.Y. Chen and F.R. Al-Solamy, Warped product bi-slant im- mersions in Kaehler manifolds, Mediterr. J. Math. 14, Art. 95, 1–11, 2017.
S. Uddin and A.Y.M. Chi, Warped product pseudo-slant submanifolds of nearly Kaehler manifolds, An. St. Univ. Ovidius Constanta, 19 (3), 195–204, 2011.
K. Yano and M. Kon, Structures on manifolds, Series in Pure Mathematics, World Scientific Publishing Co., Singapore, 1984.

Yıl 2019, Cilt: 48 Sayı: 2, 351 - 358, 01.04.2019

Falleh R. Al-solamy Siraj Uddin

Öz

Kaynakça

M. Atceken, Warped product semi-slant submanifolds in locally Riemannian product manifolds, Bull. Austral. Math. Soc. 77, 177–186, 2008.
M. Atceken, Geometry of warped product semi-invariant submanifolds of a locally Riemannian product manifold, Serdica Math. J. 35, 273–286, 2009.
M. Atceken, Warped product semi-invariant submanifolds in locally decomposable Riemannian manifolds, Hacet. J. Math. Stat. 40, 401–407, 2011.
A. Bejancu, Semi-invariant submanifolds of locally Riemannian product manifolds, Ann. Univ. Timisoara S. Math. 22, 3–11, 1984.
R.L. Bishop and B. O’Neill, Manifolds of Negative curvature, Trans. Amer. Math. Soc. 145, 1–49, 1969.
B.Y. Chen, Slant immersions, Bull. Austral. Math. Soc. 41, 135–147, 1990.
H. Li and X. Li, Semi-slant submanifolds of locally product manifolds, Georgian Math. J. 12, 273–282, 2005.
K. Matsumoto, On submanifolds of locally product Riemannian manifolds, TRU Math. 18, 145–157, 1982.
N. Papaghiuc, Semi-slant submanifolds of Kaehlerian manifold, Ann. St. Univ. Iasi, 9, 55–61, 1994.
B. Sahin, Slant submanifolds of an almost product Riemannian manifold, J. Korean Math. Soc. 43, 717–732, 2006.
B. Sahin, Warped product semi-invariant submanifolds of locally product Riemannian manifolds, Bull. Math. Soc. Sci. Math. Roumanie Tome, 49 (97), 383–394, 2006.
B. Sahin, Warped product semi-slant submanifolds of a locally product Riemannian manifold, Studia Sci. Math. Hungar. 46, 169–184, 2009.
S. Uddin and F.R. Al-Solamy, Warped product pseudo-slant submanifolds of cosymplectic manifolds, An. Ştiinţ. Univ. Al. I. Cuza Iaşi Mat. (N.S.) Tomul LXII, (f. 2,3), 901–913, 2016.
S. Uddin and F.R. Al-Solamy, Warped product pseudo-slant immersions in Sasakian manifolds, Publ. Math. Debrecen, 91 (3-4), 331–348, 2017.
S. Uddin, A. Ali, N.M. Al-Asmari and W.A. Othman, Warped product pseudo-slant submanifolds in a locally product Riemannian manifold, Diff. Geometry Dyn. Syst. 18, 147–158, 2016.
S. Uddin, B.Y. Chen and F.R. Al-Solamy, Warped product bi-slant im- mersions in Kaehler manifolds, Mediterr. J. Math. 14, Art. 95, 1–11, 2017.
S. Uddin and A.Y.M. Chi, Warped product pseudo-slant submanifolds of nearly Kaehler manifolds, An. St. Univ. Ovidius Constanta, 19 (3), 195–204, 2011.
K. Yano and M. Kon, Structures on manifolds, Series in Pure Mathematics, World Scientific Publishing Co., Singapore, 1984.

Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Konular	Matematik
Bölüm	Matematik
Yazarlar	Falleh R. Al-solamy 0000-0003-3144-570X Siraj Uddin 0000-0002-3564-6405
Yayımlanma Tarihi	1 Nisan 2019
Yayımlandığı Sayı	Yıl 2019 Cilt: 48 Sayı: 2

Kaynak Göster

APA	Al-solamy, F. R., & Uddin, S. (2019). An inequality for warped product submanifolds of a locally product Riemannian manifold. Hacettepe Journal of Mathematics and Statistics, 48(2), 351-358.
AMA	Al-solamy FR, Uddin S. An inequality for warped product submanifolds of a locally product Riemannian manifold. Hacettepe Journal of Mathematics and Statistics. Nisan 2019;48(2):351-358.
Chicago	Al-solamy, Falleh R., ve Siraj Uddin. “An Inequality for Warped Product Submanifolds of a Locally Product Riemannian Manifold”. Hacettepe Journal of Mathematics and Statistics 48, sy. 2 (Nisan 2019): 351-58.
EndNote	Al-solamy FR, Uddin S (01 Nisan 2019) An inequality for warped product submanifolds of a locally product Riemannian manifold. Hacettepe Journal of Mathematics and Statistics 48 2 351–358.
IEEE	F. R. Al-solamy ve S. Uddin, “An inequality for warped product submanifolds of a locally product Riemannian manifold”, Hacettepe Journal of Mathematics and Statistics, c. 48, sy. 2, ss. 351–358, 2019.
ISNAD	Al-solamy, Falleh R. - Uddin, Siraj. “An Inequality for Warped Product Submanifolds of a Locally Product Riemannian Manifold”. Hacettepe Journal of Mathematics and Statistics 48/2 (Nisan 2019), 351-358.
JAMA	Al-solamy FR, Uddin S. An inequality for warped product submanifolds of a locally product Riemannian manifold. Hacettepe Journal of Mathematics and Statistics. 2019;48:351–358.
MLA	Al-solamy, Falleh R. ve Siraj Uddin. “An Inequality for Warped Product Submanifolds of a Locally Product Riemannian Manifold”. Hacettepe Journal of Mathematics and Statistics, c. 48, sy. 2, 2019, ss. 351-8.
Vancouver	Al-solamy FR, Uddin S. An inequality for warped product submanifolds of a locally product Riemannian manifold. Hacettepe Journal of Mathematics and Statistics. 2019;48(2):351-8.