Skew Semi Invariant Submanifolds of Para Kenmotsu Manifold

Year 2018, , 112 - 118, 30.11.2018

Ramazan Sarı , İnan Ünal , Elif Aksoy Sarı

https://doi.org/10.17714/gumusfenbil.456858

Cited By: 1

Abstract

In this paper skew
semi invariant submanifolds of para Kenmotsu manifold are studied. An example is
given and integrability conditions of distributions are obtained. This kind of
submanifolds of para Kenmotsu space form are examined and
some
curvature properties are obtained. Finally it is proved that a totally geodesic
skew semi invariant submanifold of para Kenmotsu manifold is  -Einstein.

Keywords

Para Kenmotsu manifold, Para Kenmotsu space form, Skew semi invariant submanifolds

Para Kenmotsu Manifoldun Skew Semi İnvaryant Altmanifoldları

Abstract

Bu çalışmada para Kenmotsu
manifoldlaırn skew semi invaryant altmanifoldları çalışıldı. Bir örnek verildi
ve distribüsyonların integrallenebilirlik şartları elde edildi. Para Kenmotsu
space formun bu tür altmanifoldları incelendi ve bazı eğrilik özellikleri elde
edildi. Son olarak para Kenmotsu manifoldların bir total geoedezik skew semi
invaryant altmanifoldunun -Einstein olduğu ispatlandı.

Keywords

Para Kenmotsu manifold, Para Kenmotsu uzay form, Skew semi invariant altmanifold

References

• Adati, T. and Miyazawa, T., 1997. On para contact Riemanniann manifolds, TRU Mathematics, 13, 27-39.
• Bejancu, A. and Papaghiuc, N., 1984. Almost Semi Invariant Submanifolds of a Sasakian Manifold, Bull. Math. Soc. Sci., 28, 13-30.
• Cruceanu, V., Fortuny, P., & Gadea, P. M. (1996). A survey on paracomplex geometry. Rocky Mountain journal of mathematics, 26(1), 83-115.
• Dirik, S., Atçeken, M., and Yıldırım, Ü., 2016. Contact Pseudo Slant Submanifolds of a Kenmotsu Manifold, J. Mat. Computer Sci., 16, 386-394.
• Dirik, S., Atçeken, M., and Yıldırım, Ü., 2016. Pseudo Slant Submanifolds of Kenmotsu Space Form, Journal of Advences in Mathematics, 11(10), 5680-5696.
• Ianus, S., Mihai, I. and Matsumoto, K., 1985. Almost Semi Invariant Submanifolds of some almost para contact Riamannian Manifolds, Bull. Yamagata Univ. Natur. Sci., 11, 121-128.
• Kaneyuki, S. and Willams, F.L., 1985. Almost paracontact and parahodge structures on manifolds, Nagoya Mathematical Journal, 99, 173-187.
• Lui, X. and Shao, F.M., 1999. Skew Semi Invariant Submanifolds of a Locally Product Manifold, Portugaline Math., 56, 319-327.
• Olszak, Z., 2013. The Schouten-Van Kampen Affine Connection Adapted to an Almost Para Contact Metric Structure, Pub. de Linst. Math., 94, 31-42.
• Ronsse, G.S., 1990. Generic and Skew CR-Submanifolds of a Kaehler Manifold, Bull. Inst. Math. Acad. Sinica, 18, 127-141.
• Sato, I., 1976. On a structure similar to the almost contact structure, Tensor (N.S.), 30, 219-224.
• Sinha, B. B. and Sai Prasad, K. L., 1995. A class of almost para contact metric manifold, Bulletin of the Calcutta Mathematical Society, 87, 307-312.
• Şahin, B., 2010. Skew CR-waped product submanifolds of a Kaehler Manifolds, Math. Commun., 15, 189-204
• Turgut Vanlı, A., and Sarı, R., 2016, The smallest dimension submanifolds of para β-Kenmotsu manifold, Gazi university journal of science, 29(3), 695-701.
• Zamkovoy, S. 2009, Canonical connections on para contact manifolds, Annals of Global Analisis and Geometry, 36(1),37-60.