Totally geodesic property of the unit tangent sphere bundle with g-natural metrics

[1] K. M. T. Abbassi and G. Calvaruso, g-Natural contact metrics on unit tangent sphere bundles, Monatsh. Math., 151 (2006), 89–109.10.1007/s00605-006-0421-9Search in Google Scholar

[2] K. M. T. Abbassi and M. Sarih, On some hereditary properties of Riemannian g-natural metrics on tangent bundles of Riemannian manifolds, Diff. Geom. Appl., 22 (2005), 19–47.10.1016/j.difgeo.2004.07.003Search in Google Scholar

[3] K. M. T. Abbassi and M. Sarih, On natural metrics on tangent bundles of Riemannian manifolds, Arch. Math. (Brno), 41 (2005), 71–92.Search in Google Scholar

[4] K. M. T. Abbassi and A. Yampolsky, Transverse totally geodesic submanifolds of tangent bundle, Publ. Math. Debrecen, 64 (2004), 129–154.10.5486/PMD.2004.2909Search in Google Scholar

[5] G. Calvaruso and V. Martín-Molina, Paracontact metric structures onthe unit tangent sphere bundle, Ann. Mat. Pura Appl., 194 (2015), 1359–1380.10.1007/s10231-014-0424-4Search in Google Scholar

[6] M. Manev, Pair of associated Schouten-van Kampen connections adapted to an almost contact B-metric structure, Filomat, 10 (2015), 2437–2446.10.2298/FIL1510437MSearch in Google Scholar

[7] B. O’Neill, Semi-Riemannian geometry with applications to relativity, Acad. Press, (1983).Search in Google Scholar

[8] S. Sasaki, On the differentiable manifolds with certain structures which are closely related to almost contact structure 1, Tohoku Math. J., 12(1960), 459–476.10.2748/tmj/1178244407Search in Google Scholar

[9] P. K. Townsend and M. N. R. Wohlfarth, Cosmology as geodesic motion, Classical Quantum Gravity, 21 (2004), 53–75.10.1088/0264-9381/21/15/R01Search in Google Scholar