ON THE CONCIRCULAR CURVATURE TENSOR OF A CONTACT METRIC MANIFOLD

Title & Authors
ON THE CONCIRCULAR CURVATURE TENSOR OF A CONTACT METRIC MANIFOLD
BLAIR, D. E.; KIM, JEONG-SIK; TRIPATHI, MUKUT MANI;

Abstract
We classify N($\small{\kappa}$)-contact metric manifolds which satisfy $Z(\xi,\;X)\cdotZ\; Keywords contact metric manifold;N(K)-contact metric manifold;(K, u)-manifold;Sasakian manifold;concircular curvature tensor;concircularly sym­metric;recurrent concircular curvature tensor.; Language English Cited by 1. On Concircular Curvature Tensor with respect to the Semi-symmetric Non-metric Connection in a Kenmotsu Manifold,; Kyungpook mathematical journal, 2016. vol.56. 3, pp.951-964 2. ON Φ-RECURRENT (k, μ)-CONTACT METRIC MANIFOLDS,;;; 대한수학회보, 2008. vol.45. 4, pp.689-700 3. On N(κ)-Contact Metric Manifolds Satisfying Certain Curvature Conditions,;; Kyungpook mathematical journal, 2011. vol.51. 4, pp.457-468 4. CERTAIN SEMISYMMETRY PROPERTIES OF (𝜅, 𝜇)-CONTACT METRIC MANIFOLDS,;;; 대한수학회보, 2016. vol.53. 4, pp.1237-1247 5. ON ALMOST C(α)-MANIFOLDS SATISFYING CERTAIN CONDITIONS ON QUASI-CONFORMAL CURVATURE TENSOR,;; Proceedings of the Jangjeon Mathematical Society, 2016. vol.19. 1, pp.115-124 1. On η-Einstein Trans-Sasakian Manifolds, Annals of the Alexandru Ioan Cuza University - Mathematics, 2011, 57, 2 2. Almost Contact Metric Structures on the Hypersurface of Almost Hermitian Manifolds, Journal of Mathematical Sciences, 2015, 207, 4, 513 3. C-Bochner curvature tensor on N(k)-contact metric manifolds, Lobachevskii Journal of Mathematics, 2010, 31, 3, 209 4. Conharmonic Curvature Tensor on -Contact Metric Manifolds, ISRN Geometry, 2011, 2011, 1 5. CERTAIN SEMISYMMETRY PROPERTIES OF (𝜅, 𝜇)-CONTACT METRIC MANIFOLDS, Bulletin of the Korean Mathematical Society, 2016, 53, 4, 1237 6. On pseudo-Riemannian manifolds with recurrent concircular curvature tensor, Acta Mathematica Hungarica, 2012, 137, 1-2, 64 7. On a type of contact metric manifolds, Lobachevskii Journal of Mathematics, 2013, 34, 1, 89 8. On the M-Projective Curvature Tensor of -Contact Metric Manifolds, ISRN Geometry, 2013, 2013, 1 9. Concircular Curvature Tensor and Fluid Spacetimes, International Journal of Theoretical Physics, 2009, 48, 11, 3202 10. On a Class of α-Para Kenmotsu Manifolds, Mediterranean Journal of Mathematics, 2016, 13, 1, 391 11. On N(κ)-Contact Metric Manifolds Satisfying Certain Curvature Conditions, Kyungpook mathematical journal, 2011, 51, 4, 457 12. On Concircular Curvature Tensor with respect to the Semi-symmetric Non-metric Connection in a Kenmotsu Manifold, Kyungpook mathematical journal, 2016, 56, 3, 951 13. On the concircular curvature of a (κ,μ,ν)-manifold, Pacific Journal of Mathematics, 2014, 269, 1, 113 References 1. Ch. Baikoussis, D. E. Blair, and Th. Koufogiorgos, A decomposition of the curvature tensor of a contact manifold satisfying$R(X, Y){\varepsilon}={\kappa}({\eta}(Y)X-{\eta}(X)Y)$, Mathematics Technical Report, University of Ioannina, 1992 2. Ch. Baikoussis and Th. Koufogiorgos, On a type of contact manifolds, J. Geom. 46 (1993), 1-9 3. D. E. Blair, Riemannian geometry of contact and symplectic manifolds, Progress in Mathematics 203, Birkhauser Boston, Inc., Boston, MA, 2002 4. D. E. Blair, Two remarks on contact metric structures, Tohoku Math. J. 29 (1977), 319-324 5. D. E. Blair, Th. Koufogiorgos, and B. J. Papantoniou, Contact metric manifolds satisfying a nullity condition, Israel J. Math. 91 (1995), 189-214 6. E. Boeckx, A full classification of contact metric$({\kappa},{\mu})$-spaces, Illinois J. Math. 44 (2000), 212-219 7. M. C. Chaki and M. Tarafdar, On a type of Sasakian manifolds, Soochow J. Math. 16 (1990), 23-28 8. S. Kobayashi and K. Nomizu, Foundations of differential geometry, vol. I, Inter- science Publishers, NY, 1963 9. Z. Olszak, On contact metric manifolds, Tohoku Math. J. 31 (1979), 247-253 10. B. J. Papantoniou, Contact Riemannian manifolds satisfying$R({\varepsilon},X).R=0 and {\varepsilon}{\in}({\kappa},{\mu})$-nullity distribution, Yokohama Math. J. 40 (1993), 149-161 11. D. Perrone, Contact Riemannian manifolds satisfying$R(X,{\varepsilon}).R=0\$, Yokohama Math. J. 39 (1992), no. 2, 141-149

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