Certain Semisymmetry Curvature Conditions on Paracontact Metric (k, µ)-Manifolds

The object of the present paper is to characterize paracontact metric (k, µ)-manifolds satisfying some semisymmetry curvature conditions.

___

[1] Montano, B.C., Erken, I.K., Murathan, C.: Nullity conditions in paracontact geometry. Diff. Geom. Appl. 30, 665–693 (2012).

[2] Cartan, E.: Sur une classes remarquable d’espaces de Riemann. Bull. Soc. Math. France. 54, 214–264 (1926), .

[3] Kaneyuki, S., Williams, F.L.: Almost paracontact and parahodge structures on manifolds. Nagoya Math. J. 99, 173-187 (1985).

[4] Mandal, K., De, U.C.: Paracontact metric (k, µ)-spaces satisfying certain curvature conditions. Kyungpook Math. J. 59, 163–174 (2019).

[5] Shirokov, P. A.: Collected works of geometry. Kazan Univ. Press, Kazan (1966).

[6] Soos, G.: Über die geodätischen Abbildungen von Riemannaschen Räumen auf projektiv symmetrische Riemannsche Räume. Acta. Math. Acad. Sci. Hungar. Tom. 9, 359–361 (1958).

[7] Szabó, Z.I.: Structure theorems on Riemannian spaces satisfying R(X,Y).R=0, the local version. J. Diff. Geometry. 17, 531-582 (1982).

[8] Yano, K., Bochner, S.: Curvature and Betti numbers. Annals of Mathematics Studies, 32, Princeton University Press, (1953).

[9] Yano, K., Kon, M.: Structures on Manifolds. Series in Pure Mathematics, 3. World Scientific Publishing Co., Singapore, (1984).

[10] Yıldız, A., De, U. C.: A classification of (k, µ)-contact metric manifolds. Commun Korean Math. Soc. 27, 327–339 (2012).

[11] Zamkovoy, S.: Canonical connections on paracontact manifolds. Ann. Glob. Anal. Geom. 36, 37-60 (2009).

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