Bir Normal Hemen Hemen Parakontakt Metrik Manifoldun Quasi-Konformal Eğrilik Tensörü Üzerine

Yıl 2019, Cilt: 9 Sayı: 2, 196 - 206, 15.04.2019

Ümit Yıldırım , Mehmet Atçeken

https://doi.org/10.17714/gumusfenbil.414516

https://izlik.org/JA28SL28DT

Öz

Bu makalede bir normal
parakontak metrik manifoldun C(\xi,X)R=0, C(\xi,X)P=0, C(\xi,X)Z=0, C(\xi,X)S=0 ve C(\xi,X)C=0 şartlarını sağlaması durumunda ortaya çıkan sonuçlar çalışılmıştır. Bu
sonuçlara göre manifold karakterize edilmiştir. Burada R, Riemann eğrilik tensörü, C, quasi-konformal eğrilik tensörü, P, projektif eğrilik tensörü,  Z, concircular eğrilik tensörü ve S, Ricci tensörüdür. 

Anahtar Kelimeler

Concircular eğrilik tensörü , Einstein manifold , Normal hemen hemen parakontakt metrik manifold , Quasi-konformal eğrilik tensörü

Kaynakça

• Acet, B.E., Kılıç, E. ve Perktaş, S.Y., 2012, Some Curvature Conditions on a Para-Sasakian Manifold with Canonical Paracontact Connection, International Journal of Mathematics and Mathematical Sciences, Volume 2012, Article ID 395462, 24 pages.
• Acet, B.E. ve Perktaş, S.Y., 2016. On para-Sasakian manifolds with a canonical paracontact connection, New Trends in Math. Sci. 4, No. 3, 162-173, 2016.
• Atçeken, M., 2013. Some curvature properties of 〖(LCS)〗_n-manifolds. Abstract and Applied Analysis, Doi: 10.1055/2013/380657.
• Atçeken, M. ve Yıldırım, Ü., 2016. On an almost C(α)-manifolds satisfying certain conditions on quasi-conformal curvature tensor. Proceedings of the Jangjeon Mathematical Society, 19 (1), 115-124. Atçeken, M., Dirik, S. ve Yıldırım, Ü., 2017. An Inequality for Warped Product Semi-Invariant Submanifolds of a Normal Paracontact Metric Manifold. Filomat 31:19, 6233–6240.
• Atçeken, M., Yıldırım, Ü. ve Dirik, S., 2017. Sub-Manifolds of a Riemannian Manifold. Manifolds: Current Research Areas, Prof. Paul Bracken, InTech, DOI: 10.5772/65948.
• Boothby, W.M., 1986. An Introduction to Differentiable Manifolds and Riemanniann Geometry. Academic Press, Inc. London.
• De, U.C., Jun, J.B., ve Gazi, A.K., 2008. Sasakian manifolds with quasi-conformal curvature tensor. Bulletin of the Korean Mathematical Society, 45 (2) 313-319.
• De, U.C., ve Mondal, A.K., 2009. On 3-dimensional normal almost contact metric manifolds satisfying certain curvature conditions. Commun. Korean. Math. Soc., 24, 265-275.
• De, U.C., ve Sarkar, A., 2012. On the quasi-conformal curvature tensor of (κ,μ)-contact metric manifold. Mathematical Reports, 14 (2) 115-129.
• De, U.C., Yıldız, A., ve Yalınız, A.F., 2009. Locally ϕ-symmetric normal almost contact metric manifolds of dimension 3. Appl. Math. Lett., 22, 723-727.
• Erdem, S., 2002. On almost (para)contact (hyperbolic) metric manifolds and harmonicity of (ϕ,ϕ^' )-holomorphic maps between them. Houston J. Math., 28, 21-45.
• Erken, İ.K., 2015. On normal almost paracontact metric manifolds of dimension 3. Facta Universitatis (NIS), Ser. Math. Inform., 30 (5) 777-788.
• Hosseinzadeh, A., ve Taleshian, A., 2012. On conformal and quasi conformal curvature tensors of an N(k)-quasi Einstein manifold. Communucations of the KMS, 27 (2), 317-326.
• Sato, I., 1976. On a structure similar to the almost contact structure, Tensor (N.S.), 30, no. 3, 219-224.
• Sato, I., 1977. On a structure similar to almost contact structures II, Tensor (N.S.), 31, no. 2, 199-205.
• Kaneyuki, S., ve Williams, F.L., 1985. Almost paraccontact and parahodge structures on manifolds. Nagoya Math. J., 99, 173-187.
• Martin, M.V., 2015. On a remarkable class of paracontact metric manifolds. International Journal of Geometric Methods in Modern Physics, 12 (8).
• Olszak, Z., 1986. Normal almost contact metric manifolds of dimension three. Ann. Polon. Math., XLVII, 41-50. O’Neill, B., 1983. Semi-Riemann Geometry with Applications to Relativity. Pure and Applied Mathematics, 103, Academ,c Press, Inc. New York.
• Pandey, H.B. ve Kumar, A., 1985. Anti invariant submanifolds of almost paracontact manifolds. Indian J. Püre appl. Math., 16(6), 586-590.
• Szabo, Z.I., 1982. Structure theorems on Riemannian spaces satisfying R(X,Y)R=0 the local version. Diff. Geom., 17, 531-582.
• Yano, K., ve Kon, M., 1984. Structres on Manifolds. Series in Pure Mathematics, 3, World Scientific Publishing Co., Singapore, 72.
• Yıldırım, Ü., Atçeken, M. ve Dirik, S. 2018. B-Y. Chen Inequalities for Semi-Slant Submanifolds in Normal Paracontact Metric Manifolds. Palestine Journal of Mathematics, Vol. 7(1)(2018) , 281-288.