The ℳ-projective curvature tensor field on generalized (κ,μ)-paracontact metric manifolds

References

[1] G. Calvaruso, Homogeneous paracontact metric three-manifolds, Illinois J. Math. 55 (2011), no. 2, 697–718. 10.1215/ijm/1359762409Search in Google Scholar

[2] G. Calvaruso and A. Perrone, Ricci solitons in three-dimensional paracontact geometry, J. Geom. Phys. 98 (2015), 1–12. 10.1016/j.geomphys.2015.07.021Search in Google Scholar

[3] G. Calvaruso and D. Perrone, Geometry of H-paracontact metric manifolds, Publ. Math. Debrecen 86 (2015), no. 3–4, 325–346. 10.5486/PMD.2015.6078Search in Google Scholar

[4] B. Cappelletti-Montano, Bi-Legendrian structures and paracontact geometry, Int. J. Geom. Methods Mod. Phys. 6 (2009), no. 3, 487–504. 10.1142/S0219887809003631Search in Google Scholar

[5] B. Cappelletti-Montano and L. Di Terlizzi, Geometric structures associated to a contact metric (κ,μ)-space, Pacific J. Math. 246 (2010), no. 2, 257–292. 10.2140/pjm.2010.246.257Search in Google Scholar

[6] B. Cappelletti-Montano, I. Küpeli Erken and C. Murathan, Nullity conditions in paracontact geometry, Differential Geom. Appl. 30 (2012), no. 6, 665–693. 10.1016/j.difgeo.2012.09.006Search in Google Scholar

[7] S. K. Chaubey and R. H. Ojha, On the m-projective curvature tensor of a Kenmotsu manifold, Differ. Geom. Dyn. Syst. 12 (2010), 52–60. Search in Google Scholar

[8] V. Cortés, M.-A. Lawn and L. Schäfer, Affine hyperspheres associated to special para-Kähler manifolds, Int. J. Geom. Methods Mod. Phys. 3 (2006), no. 5–6, 995–1009. 10.1142/S0219887806001569Search in Google Scholar

[9] P. Dacko and Z. Olszak, On weakly para-cosymplectic manifolds of dimension 3, J. Geom. Phys. 57 (2007), no. 2, 561–570. 10.1016/j.geomphys.2006.05.001Search in Google Scholar

[10] U. C. De and P. Pal, On generalized M-projectively recurrent manifolds, Ann. Univ. Paedagog. Crac. Stud. Math. 13 (2014), 77–101. Search in Google Scholar

[11] S. Erdem, On almost (para)contact (hyperbolic) metric manifolds and harmonicity of (ϕ,ϕ′)-holomorphic maps between them, Houston J. Math. 28 (2002), no. 1, 21–45. Search in Google Scholar

[12] S. Ivanov, D. Vassilev and S. Zamkovoy, Conformal paracontact curvature and the local flatness theorem, Geom. Dedicata 144 (2010), 79–100. 10.1007/s10711-009-9388-8Search in Google Scholar

[13] S. Kaneyuki and F. L. Williams, Almost paracontact and parahodge structures on manifolds, Nagoya Math. J. 99 (1985), 173–187. 10.1017/S0027763000021565Search in Google Scholar

[14] I. Küpeli Erken, Generalized (κ~≠-1,μ~)-paracontact metric manifolds with ξ⁢(μ~)=0, Int. Electron. J. Geom. 8 (2015), no. 1, 77–93. Search in Google Scholar

[15] I. Küpeli Erken and C. Murathan, A study of three dimensional paracontact (κ~,μ~,ν~)-spaces, Int. J. Geom. Methods Mod. Phys. 14 (2017), no. 7, 1750106. Search in Google Scholar

[16] R. H. Ojha, A note on the M-projective curvature tensor, Indian J. Pure Appl. Math. 8 (1977), no. 12, 1531–1534. Search in Google Scholar

[17] R. H. Ojha, M-projectively flat Sasakian manifolds, Indian J. Pure Appl. Math. 17 (1986), no. 4, 481–484. Search in Google Scholar

[18] G. P. Pokhariyal and R. S. Mishra, Curvature tensors and their relativistic significance. II, Yokohama Math. J. 19 (1971), no. 2, 97–103. Search in Google Scholar

[19] D. G. Prakasha and K. K. Mirji, On (κ,μ)-paracontact metric manifolds, Gen. Math. Notes 25 (2014), no. 2, 68–77. Search in Google Scholar

[20] D. G. Prakasha and K. K. Mirji, On ϕ-symmetric N⁢(k)-paracontact metric manifolds, J. Math. 2015 (2015), Article ID 728298. 10.1155/2015/728298Search in Google Scholar

[21] I. Sato, On a structure similar to the almost contact structure, Tensor (N. S.) 30 (1976), no. 3, 219–224. Search in Google Scholar

[22] S. Zamkovoy, Canonical connections on paracontact manifolds, Ann. Global Anal. Geom. 36 (2009), no. 1, 37–60. 10.1007/s10455-008-9147-3Search in Google Scholar

[23] S. Zamkovoy and V. Tzanov, Non-existence of flat paracontact metric structures in dimension greater than or equal to five, Annuaire Univ. Sofia Fac. Math. Inform. 100 (2011), 27–34. Search in Google Scholar