Some curvature properties of 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] B. Cappelletti Montano, Bi-paracontact structures and Legendre foliations, Kodai Math. J. 33 (2010), no. 3, 473–512. 10.2996/kmj/1288962554Search in Google Scholar

[3] B. Cappelletti-Montano, A. Carriazo and V. Martín-Molina, Sasaki–Einstein and paraSasaki–Einstein metrics from (κ,μ)-structures, J. Geom. Phys. 73 (2013), 20–36. 10.1016/j.geomphys.2013.05.001Search in Google Scholar

[4] 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

[5] 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

[6] U. C. De, Second order parallel tensors on P-Sasakian manifolds, Publ. Math. Debrecen 49 (1996), no. 1–2, 33–37. 10.5486/PMD.1996.1596Search in Google Scholar

[7] U. C. De, S. Deshmukh and K. Mandal, On three-dimensional N⁢(k)-paracontact metric manifolds and Ricci solitons, Bull. Iranian Math. Soc., to appear. Search in Google Scholar

[8] U. C. De and K. Mandal, Certain results on generalized (k,μ)-contact metric manifolds, J. Geom. 108 (2017), no. 2, 611–621. 10.1007/s00022-016-0362-ySearch in Google Scholar

[9] L. P. Eisenhart, Symmetric tensors of the second order whose first covariant derivatives are zero, Trans. Amer. Math. Soc. 25 (1923), no. 2, 297–306. 10.1090/S0002-9947-1923-1501245-6Search in Google Scholar

[10] 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

[11] H. Levy, Symmetric tensors of the second order whose covariant derivatives vanish, Ann. of Math. (2) 27 (1925), no. 2, 91–98. 10.2307/1967964Search in Google Scholar

[12] V. Martín-Molina, Local classification and examples of an important class of paracontact metric manifolds, Filomat 29 (2015), no. 3, 507–515. 10.2298/FIL1503507MSearch in Google Scholar

[13] V. A. Mirzoyan, Structure theorems for Riemannian Ric-semisymmetric spaces, Izv. Vyssh. Uchebn. Zaved. Mat. (1992), no. 6, 80–89. Search in Google Scholar

[14] R. Sharma, Second order parallel tensors on contact manifolds, Algebras Groups Geom. 7 (1990), no. 2, 145–152. Search in Google Scholar

[15] P. A. Shirokov, Constant vector fields and tensor fields of second order in Riemannian spaces, Izv. Kazan Fiz. Mat. Obshchestva Ser 25 (1925), 86–114. Search in Google Scholar

[16] Z. I. Szabó, Structure theorems on Riemannian spaces satisfying R⁢(X,Y)⋅R=0. I. The local version, J. Differential Geom. 17 (1982), no. 4, 531–582. Search in Google Scholar

[17] P. Verheyen and L. Verstraelen, A new intrinsic characterization of hypercylinders in Euclidean spaces, Kyungpook Math. J. 25 (1985), no. 1, 1–4. Search in Google Scholar

[18] Y. Wang and X. Liu, Second order parallel tensors on almost Kenmotsu manifolds satisfying the nullity distributions, Filomat 28 (2014), no. 4, 839–847. 10.2298/FIL1404839WSearch in Google Scholar

[19] 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