SOME CLASSES OF 3-DIMENSIONAL NORMAL ALMOST PARACONTACT METRIC MANIFOLDS

• Journal title : Honam Mathematical Journal
• Volume 37, Issue 4,  2015, pp.457-468
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2015.37.4.457
Title & Authors
SOME CLASSES OF 3-DIMENSIONAL NORMAL ALMOST PARACONTACT METRIC MANIFOLDS
ERKEN, I. KUPELI;

Abstract
The aim of present paper is to investigate 3-dimensional $\small{{\xi}}$-projectively flt and $\small{\tilde{\varphi}}$-projectively flt normal almost paracontact metric manifolds. As a first step, we proved that if the 3-dimensional normal almost paracontact metric manifold is $\small{{\xi}}$-projectively flt then ${\Delta}{\beta} Keywords normal almost paracontact metric manifold;curvarure tensor;$\small{{\xi}}$-projectively flat;$\small{{\varphi}}$-projectively flat;para-Sasakian manifold;Einstein manifold; Language English Cited by References 1. D.V. Alekseevski, V. Cortes, A.S. Galaev, T. Leistner, Cones over pseudo-Riemannian manifolds and their holonomy, J. Reine Angew. Math. 635 (2009), 23-69. 2. D.V. Alekseevski, C. Medori, A. Tomassini, Maximally homogeneous para-CR manifolds, Ann. Glob. Anal. Geom. 30 (2006), 1-27. 3. C. L. Bejan, M. Crasmareanu, Second order parallel tensors and Ricci solitons in 3-dimensional normal paracontact geometry, Ann. Global Anal. Geom. 46(2) (2014), 117-127. 4. D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Progress in Mathematics Vol. 203, Birkhauser, Boston, 2002. 5. B. Cappelletti-Montano, I. Kupeli Erken, C. Murathan, Nullity conditions in paracontact geometry, Diff. Geom. Appl. 30 (2012), 665-693. 6. V. Cortes, C. Mayer, T. Mohaupt, F. Saueressing, Special geometry of Euclidean supersymmetry, 1. Vector multiplets. J. High Energy Phys. (2004) 03:028: 73. 7. V. Cortes, M.A. Lawn, L. Schafer, Affine hyperspheres associated to special para-Kahler manifolds, Int. J. Geom. Methods Mod. Phys. 3 (2006), 995-1009. 8. P. Dacko, On almost para-cosymplectic manifolds, Tsukuba J. Math. 28 (2004), 193-213. 9. U.C. De, A. K. Mondal, The structure of some classes of 3-dimensional normal almost contact metric manifolds, Bull. Malays. Math. Sci. Soc. 36 (2) (2013), 501-509. 10. S. Erdem, On almost (para)contact (hyperbolic) metric manifolds and harmonicity of (${\phi},{\varphi}'$)-holomorphic maps between them, Houston J. Math. 28 (2002), 21-45. 11. S. Kaneyuki , F. L.Williams, Almost paracontact and parahodge structures on manifolds, Nagoya Math. J. 99 (1985), 173-187. 12. I. Kupeli Erken, C. Murathan, A Complete Study of Three-Dimensional Paracontact (${\kappa},{\mu},{\nu}\$)-spaces, Submitted. Available in Arxiv:1305.1511 [math. DG].

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