On a Class of Submanifolds in a Tangent Bundle with a g-Natural Metric - Normal lift

Year 2019, Volume: 12 Issue: 2, 144 - 156, 03.10.2019

Stanisław Ewert-krzemieniewski

https://doi.org/10.36890/iejg.628065

Abstract

Keywords

Riemannian manifold, tangent bundle, g-natural metric, submanifold, isometric immersion, totally geodesic distribution, non-degenerate metric

References

• [1] Abbassi, M. T. K., Yampolsky, A., Transverse totally geodesic submanifolds of the tangent bundle. Publ. Math. Debrecen 64/1-2 (2004), 129-154.
• [2] Abbassi, M. T. K., Sarih, Maâti, On natural metrics on tangent bundles of Riemannian manifolds. Arch. Math. (Brno) 41 (2005), no. 1, 71–92.
• [3] Abbassi, M. T. K., Sarih, Maâti, On some hereditary properties of Riemannian g-natural metrics on tangent bundles of Riemannian manifolds. Differential Geom. Appl. 22 (2005), no. 1, 19–47.
• [4] Abbassi, M. T. K., Métriques Naturelles Riemanniennes sur la Fibré tangent une variété Riemannienne, Editions Universitaires Européénnes, Saarbrücken, Germany, 2012.
• [5] Degla, S., Ezin, J. P., Todjihounde, L., On g-natural metrics of constant sectional curvature on tangent bundles. Int. Electronic J. Geom. 2(1) (2009), p. 74-94.
• [6] Deshmukh S., Al-Odan, H., Shaman, T. A., Tangent bundle of the hypersurfaces in a Euclidean space. Acta Math. Acad. Pedagog. Nyíregyháziensis 23(1) (2007),71-87.
• [7] Dombrowski, P., On the Geometry of Tangent Bundle. J. Reine Angew. Math. 210 (1962), p. 73-88.
• [8] Ewert-Krzemieniewski, S., On a classification of Killing vector fields on a tangent bundle with g-natural metric. arXiv:1305:3817v1.
• [9] Ewert-Krzemieniewski, S., On a Killing vector fields on a tangent bundle with g-natural metric Part I. Note Mat. 34 no. 2, (2014), 107-133.
• [10] Ewert-Krzemieniewski, S., Totally geodesic submanifolds in tangent bundle with g-natural metric. Int. J. Geom. Methods Mod. Phys. 11 (2014), no. 9, 1460033 (9 pages).
• [11] Ewert-Krzemieniewski, S., On a class of submanifolds in tangent bundle with g-natural metric. arXiv:1411.3274.
• [12] Ewert-Krzemieniewski, S., On a class of submanifolds in a tangent bundle with a g-natural metric. Coll. Math., 150 no.1, (2017), 121-133.
• [13] Kowalski, O., Sekizawa, M., Natural transformations of Riemannian metrics on manifolds to metrics on tangent bundles, A classification. Bull. Tokyo Gakugei Univ. (4) 40 (1988), 1–29.
• [14] Yano, K., Kon, M., Structures on Manifolds. World Scientific, 1984.
• [15] Yano, K., Ishihara, S., Tangent and cotangent bundles. Marcel Dekker, Inc. New York, 1973.
• [16] Yano, K., Submanifolds with parallel mean curvature vector. J. Diff. Geom. 6 (1971), 95-118.