SOME CURVATURE PROPERTIES ON PARACONTACT METRIC (k;μ)-MANIFOLDS WITH RESPECT TO THE SCHOUTEN-VAN KAMPEN CONNECTION
Abstract
The object of the present paper is to characterize paracontact metric (k;μ)-manifolds satisfying certain semisymmetry curvature conditions with respect to the Schouten-van Kampen connection.
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Bejancu A. and Faran H., Foliations and geometric structures, Math. and its appl., 580, Springer, Dordrecht, 2006.
BlairD.E., Koufogiorgos T., Papantoniou B.J., Contact metric manifolds satisfying a nullity condition, Israel J. Math. 91(1995), 189-214.
Cappelletti-Montano B., Erken I. Küpeli , Murathan C., Nullity conditions in paracontact geometry, Di¤. Geom. Appl.30(2012), 665-693.
Hamilton R. S., The Ricci ‡ow on surfaces, Mathematics and general relativity (Santa Cruz,CA, 1986), 237-262, Contemp. Math. 71, American Math. Soc., 1988.
Ianu¸s S., Some almost product structures on manifolds with linear connection, Kodai Math. Sem. Rep.,23(1971), 305-310.
KaneyukiS., Williams F.L., Almost paracontact and parahodge structures on manifolds, Nagoya Math. J.,99(1985), 173-187.
Mandal K., De U. C., Paracontact metric (k;)-spaces satisfying certain curvature conditions, Kyungpook Math. J.,59(2019), 163-174.
Mirzoyan V. A., Structure theorems on Riemannian Ricci semisymmetric spaces, Izv. Vyssh. Uchebn. Zaved. Mat.,6(1992), 80-89, (in Russian).
Olszak Z., The Schouten-van Kampen a¢ ne connection adapted an almost (para) contact metric structure, Publ. De L’inst. Math.,94(2013), 31-42.
Perelman G., The entopy formula for the Ricci ‡ow and its geometric applications, Preprint, http://arxiv.org/abs/math.DG/02111159.
Schouten J. and van Kampen E., Zur Einbettungs-und Krümmungsthorie nichtholonomer Gebilde, Math. Ann.,103(1930), 752-783.
Sharma R., Certain results on K-contact and (k;)-contact manifolds, Journal of Geometry, 89(2008), 138-147.
Solov’ev A. F., On the curvature of the connection induced on a hyperdistribution in a Riemannian space, Geom. Sb.,19(1978), 12-23, (in Russian).
— — — — , The bending of hyperdistributions, Geom. Sb.,20(1979), 101-112, (in Russian).
— — — — , Second fundamental form of a distribution, Mat. Zametki,35(1982), 139-146.
— — — — , Curvature of a distribution, Mat. Zametki,35(1984), 111-124.
Szabo Z., Structure theorems on Riemannian spaces satisfying R(X,Y).R=0, The local version,
J. Di¤erential Geometry,17(1982), 531-582.
Yildiz A., De U. C., A classi…cation of (k,mu)-contact metric manifolds, Commun Korean
Math. Soc.,27(2012), 327-339.
Yildiz A., De U. C., Certain semisymmetry curvature conditions on paracontact metric (k,mu)-manifolds, Math. Sci. App. E-notes,8(1)(2020), 1-10.
Zamkovoy S., Canonical connections on paracontact manifolds, Ann. Glob. Anal. Geom., 36(2009), 37-60.
Zamkovoy S., Tzanov V., Non-existence of ‡at paracontact metric structures in dimension greater than or equal to …ve, Annuaire Univ. So…a Fac. Math. Inform. 100(2011),
-34.
DOI: https://doi.org/10.22190/FUMI200915029Y
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