On invariant submanifolds of Riemannian warped product manifold

ŞAHİN, B.; ATÇEKEN, M.; KILIÇ, E.

On invariant submanifolds of Riemannian warped product manifold

M. ATÇEKEN, (İnönü Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Malatya, Türkiye)

B. ŞAHİN, (Girilmedi)

E. KILIÇ (Girilmedi)

Turkish Journal of Mathematics

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Yıl: 2003 Cilt: 27 Sayı: 3 Sayfa Aralığı: 407 - 423 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

On invariant submanifolds of Riemannian warped product manifold

Öz:

In this paper, we generalize the geometry of the invariant submanifolds of Riemannian product manifold to the geometry of the invariant submanifolds of Riemannian warped product manifold. We investigate some properties of an invariant submanifolds of a Riemannian warped product manifold. We show that every invariant submanifold of the Riemannian warped product manifold is a Riemannian warped product manifold. Also, we give a theorem on the pseudo-umbilical invariant submanifold. Further, we obtain that integral manifolds on an invariant submanifold are curvature-invariant submanifolds. Finally, we give a necessary condititon on a totally umbilical invariant submanifold to be totally geodesic.

Anahtar Kelime:

Konular: Matematik

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1] Atceken, M., and Keles, S., On the Product Riemannian Manifold. Differential Geometry-Dynamical Systems. Vol.5/2003. pp.1-7.
[2] Bejancu, A., Semi-Invariant Submanifolds of Locally Product Riemannian Manifolds, An. Univ. Timişoara Ser. Ştiint. Mat. 22(1984)3-11.
[3] Chen, B.Y.,Geometry of Submanifolds. Marcel Dekker Inc., New York(1973).
[4] Chen, B.Y., Total Mean Curvature and Submanifolds of Finite Type. World Scientific Publishing Co Pte Ltd. (1984).
[5] Matsumoto, K., On Submanifolds of Locally Product Riemannian Manifolds, TRU Mathematics 18-2(1982),145-157.
[6] Senlin, X., and Yilong.N., Submanifolds of Product Riemannian Manifold. Acta Mathematica Scientia 2000,20(B)213-218.
[7] O'Neill, B., Semi-Riemannian Geometry, Academic Press. Inc(1983).

APA	ATÇEKEN M, ŞAHİN B, KILIÇ E (2003). On invariant submanifolds of Riemannian warped product manifold. , 407 - 423.
Chicago	ATÇEKEN M.,ŞAHİN B.,KILIÇ E. On invariant submanifolds of Riemannian warped product manifold. (2003): 407 - 423.
MLA	ATÇEKEN M.,ŞAHİN B.,KILIÇ E. On invariant submanifolds of Riemannian warped product manifold. , 2003, ss.407 - 423.
AMA	ATÇEKEN M,ŞAHİN B,KILIÇ E On invariant submanifolds of Riemannian warped product manifold. . 2003; 407 - 423.
Vancouver	ATÇEKEN M,ŞAHİN B,KILIÇ E On invariant submanifolds of Riemannian warped product manifold. . 2003; 407 - 423.
IEEE	ATÇEKEN M,ŞAHİN B,KILIÇ E "On invariant submanifolds of Riemannian warped product manifold." , ss.407 - 423, 2003.
ISNAD	ATÇEKEN, M. vd. "On invariant submanifolds of Riemannian warped product manifold". (2003), 407-423.

APA	ATÇEKEN M, ŞAHİN B, KILIÇ E (2003). On invariant submanifolds of Riemannian warped product manifold. Turkish Journal of Mathematics, 27(3), 407 - 423.
Chicago	ATÇEKEN M.,ŞAHİN B.,KILIÇ E. On invariant submanifolds of Riemannian warped product manifold. Turkish Journal of Mathematics 27, no.3 (2003): 407 - 423.
MLA	ATÇEKEN M.,ŞAHİN B.,KILIÇ E. On invariant submanifolds of Riemannian warped product manifold. Turkish Journal of Mathematics, vol.27, no.3, 2003, ss.407 - 423.
AMA	ATÇEKEN M,ŞAHİN B,KILIÇ E On invariant submanifolds of Riemannian warped product manifold. Turkish Journal of Mathematics. 2003; 27(3): 407 - 423.
Vancouver	ATÇEKEN M,ŞAHİN B,KILIÇ E On invariant submanifolds of Riemannian warped product manifold. Turkish Journal of Mathematics. 2003; 27(3): 407 - 423.
IEEE	ATÇEKEN M,ŞAHİN B,KILIÇ E "On invariant submanifolds of Riemannian warped product manifold." Turkish Journal of Mathematics, 27, ss.407 - 423, 2003.
ISNAD	ATÇEKEN, M. vd. "On invariant submanifolds of Riemannian warped product manifold". Turkish Journal of Mathematics 27/3 (2003), 407-423.