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

Abstract

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.
Year 2019, Volume: 12 Issue: 2, 144 - 156, 03.10.2019
https://doi.org/10.36890/iejg.628065

Abstract

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.
There are 16 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Stanisław Ewert-krzemieniewski This is me

Publication Date October 3, 2019
Published in Issue Year 2019 Volume: 12 Issue: 2

Cite

APA Ewert-krzemieniewski, S. (2019). On a Class of Submanifolds in a Tangent Bundle with a g-Natural Metric - Normal lift. International Electronic Journal of Geometry, 12(2), 144-156. https://doi.org/10.36890/iejg.628065
AMA Ewert-krzemieniewski S. On a Class of Submanifolds in a Tangent Bundle with a g-Natural Metric - Normal lift. Int. Electron. J. Geom. October 2019;12(2):144-156. doi:10.36890/iejg.628065
Chicago Ewert-krzemieniewski, Stanisław. “On a Class of Submanifolds in a Tangent Bundle With a G-Natural Metric - Normal Lift”. International Electronic Journal of Geometry 12, no. 2 (October 2019): 144-56. https://doi.org/10.36890/iejg.628065.
EndNote Ewert-krzemieniewski S (October 1, 2019) On a Class of Submanifolds in a Tangent Bundle with a g-Natural Metric - Normal lift. International Electronic Journal of Geometry 12 2 144–156.
IEEE S. Ewert-krzemieniewski, “On a Class of Submanifolds in a Tangent Bundle with a g-Natural Metric - Normal lift”, Int. Electron. J. Geom., vol. 12, no. 2, pp. 144–156, 2019, doi: 10.36890/iejg.628065.
ISNAD Ewert-krzemieniewski, Stanisław. “On a Class of Submanifolds in a Tangent Bundle With a G-Natural Metric - Normal Lift”. International Electronic Journal of Geometry 12/2 (October 2019), 144-156. https://doi.org/10.36890/iejg.628065.
JAMA Ewert-krzemieniewski S. On a Class of Submanifolds in a Tangent Bundle with a g-Natural Metric - Normal lift. Int. Electron. J. Geom. 2019;12:144–156.
MLA Ewert-krzemieniewski, Stanisław. “On a Class of Submanifolds in a Tangent Bundle With a G-Natural Metric - Normal Lift”. International Electronic Journal of Geometry, vol. 12, no. 2, 2019, pp. 144-56, doi:10.36890/iejg.628065.
Vancouver Ewert-krzemieniewski S. On a Class of Submanifolds in a Tangent Bundle with a g-Natural Metric - Normal lift. Int. Electron. J. Geom. 2019;12(2):144-56.