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Skew Semi Invariant Submanifolds of Para Kenmotsu Manifold

Year 2018, , 112 - 118, 30.11.2018
https://doi.org/10.17714/gumusfenbil.456858

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
s
ome
curvature properties are obtained. Finally it is proved that a totally geodesic
skew semi
invariant submanifold of para Kenmotsu manifold is  -Einstein.

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.

Para Kenmotsu Manifoldun Skew Semi İnvaryant Altmanifoldları

Year 2018, , 112 - 118, 30.11.2018
https://doi.org/10.17714/gumusfenbil.456858

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.

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.
There are 15 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Ramazan Sarı 0000-0002-4618-8243

İnan Ünal 0000-0003-1318-9685

Elif Aksoy Sarı This is me 0000-0003-4377-4148

Publication Date November 30, 2018
Submission Date September 3, 2018
Acceptance Date November 30, 2018
Published in Issue Year 2018

Cite

APA Sarı, R., Ünal, İ., & Aksoy Sarı, E. (2018). Skew Semi Invariant Submanifolds of Para Kenmotsu Manifold. Gümüşhane Üniversitesi Fen Bilimleri Dergisi112-118. https://doi.org/10.17714/gumusfenbil.456858

Cited By

SKEW SEMI-INVARIANT SUBMANIFOLDS OF GENERALIZED KENMOTSU MANIFOLDS
Journal of Engineering Technology and Applied Sciences
İ̇nan ÜNAL
https://doi.org/10.30931/jetas.836111