Research Article
BibTex RIS Cite

ON KILLING VECTOR FIELDS ON A TANGENT BUNDLE WITH g-NATURAL METRIC

Year 2015, Volume: 8 Issue: 1, 53 - 76, 30.04.2015
https://doi.org/10.36890/iejg.592798

Abstract

  

References

  • [1] Abbassi, M. T. K., M´etriques Naturelles Riemanniennes sur la Fibr´e tangent une vari´et´e Riemannienne, Editions Universitaires Europ´e´ennes, Saarbrücken, Germany, 2012.
  • [2] Abbassi, M. T. K.,g− natural metrics: new horizons in the geometry of tangent bundles of Riemannian manifolds, Note di Matematica, 1 (2008), suppl. n. 1, 6-35.
  • [3] Abbassi, M. T. K., Sarih, M., Killing vector fields on tangent bundle with Cheeger-Gromoll metric, Tsukuba J. Math., 27 no. 2, (2003), 295-306.
  • [4] Abbassi, M. T. K., Sarih, Maaˆti, On natural metrics on tangent bundles of Riemannian manifolds, Arch. Math. (Brno) 41 (2005), no. 1, 71–92.
  • [5] Abbassi, M. T. K., Sarih, Maaˆti, On some hereditary properties of Riemannian g− natural metrics on tangent bundles of Riemannian manifolds, Differential Geom. Appl. 22 (2005), no. 1, 19–47.
  • [6] Belkhelfa, M., Deszcz, R., G-logowska, M., Hotlo´s, M., Kowalczyk, D., Verstraelen, L., On some type of curvature conditions, in: PDEs, Submanifolds and Affine Differential Geometry, Banach Center Publ. 57, Inst. Math., Polish Acad. Sci., 2002, 179-194.
  • [7] 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), 74-94.
  • [8] Dombrowski, P., On the Geometry of Tangent Bundle, J. Reine Angew. Math., 210 (1962), 73-88.
  • [9] Ewert-Krzemieniewski, S., On 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., On a classification of Killing vector fields on a tangent bundle with g− natural metric, arXiv:1305:3817v1.
  • [11] Ewert-Krzemieniewski, S., Totally umbilical submanifolds in some semi-Riemannian mani- folds, Coll. Math., 119 no. 2, (2010), 269-299.
  • [12] Grycak, W., On generalized curvature tensors and symmetric (0,2)-tensors with symmetry condition imposed on the second derivative, Tensor N.S., 33 no. 2, (1979), 150-152.
  • [13] Gudmundsson, S., Kappos, E., On the Geometry of Tangent Bundles, Expo. Math., 20 (2002), 1-41.
  • [14] Kobayashi, S., Nomizu, K., Fundations of Differential Geometry, Vol. I, 1963.
  • [15] 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.
  • [16] Nomizu, K., On the decomposition of generalized curvature tensor fields, Differential geom- etry in honor of K. Yano, Kinokuniya, Tokyo, (1972), 335-345.
  • [17] Tanno, S., Infinitesimal isometries on the tangent bundles with complete lift metric, Tensor, N.S., 28 (1974), 139-144.
  • [18] Tanno, S., Killing vectors and geodesic flow vectors on tangent bundle, J. Reine Angew. Math, 238 (1976), 162-171.
  • [19] Walker, A. G., On Ruse’s spaces of recurrent curvature, Proc. Lond. Math. Soc., 52 (1950), 36-64.
  • [20] Yano, K., Integrals Formulas in Riemannian Geometry, Marcel Dekker, Inc. New York, 1970. ara, S., Tangent and cotangent bundles, Marcel Dekker, Inc. New York, 1973.
Year 2015, Volume: 8 Issue: 1, 53 - 76, 30.04.2015
https://doi.org/10.36890/iejg.592798

Abstract

References

  • [1] Abbassi, M. T. K., M´etriques Naturelles Riemanniennes sur la Fibr´e tangent une vari´et´e Riemannienne, Editions Universitaires Europ´e´ennes, Saarbrücken, Germany, 2012.
  • [2] Abbassi, M. T. K.,g− natural metrics: new horizons in the geometry of tangent bundles of Riemannian manifolds, Note di Matematica, 1 (2008), suppl. n. 1, 6-35.
  • [3] Abbassi, M. T. K., Sarih, M., Killing vector fields on tangent bundle with Cheeger-Gromoll metric, Tsukuba J. Math., 27 no. 2, (2003), 295-306.
  • [4] Abbassi, M. T. K., Sarih, Maaˆti, On natural metrics on tangent bundles of Riemannian manifolds, Arch. Math. (Brno) 41 (2005), no. 1, 71–92.
  • [5] Abbassi, M. T. K., Sarih, Maaˆti, On some hereditary properties of Riemannian g− natural metrics on tangent bundles of Riemannian manifolds, Differential Geom. Appl. 22 (2005), no. 1, 19–47.
  • [6] Belkhelfa, M., Deszcz, R., G-logowska, M., Hotlo´s, M., Kowalczyk, D., Verstraelen, L., On some type of curvature conditions, in: PDEs, Submanifolds and Affine Differential Geometry, Banach Center Publ. 57, Inst. Math., Polish Acad. Sci., 2002, 179-194.
  • [7] 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), 74-94.
  • [8] Dombrowski, P., On the Geometry of Tangent Bundle, J. Reine Angew. Math., 210 (1962), 73-88.
  • [9] Ewert-Krzemieniewski, S., On 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., On a classification of Killing vector fields on a tangent bundle with g− natural metric, arXiv:1305:3817v1.
  • [11] Ewert-Krzemieniewski, S., Totally umbilical submanifolds in some semi-Riemannian mani- folds, Coll. Math., 119 no. 2, (2010), 269-299.
  • [12] Grycak, W., On generalized curvature tensors and symmetric (0,2)-tensors with symmetry condition imposed on the second derivative, Tensor N.S., 33 no. 2, (1979), 150-152.
  • [13] Gudmundsson, S., Kappos, E., On the Geometry of Tangent Bundles, Expo. Math., 20 (2002), 1-41.
  • [14] Kobayashi, S., Nomizu, K., Fundations of Differential Geometry, Vol. I, 1963.
  • [15] 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.
  • [16] Nomizu, K., On the decomposition of generalized curvature tensor fields, Differential geom- etry in honor of K. Yano, Kinokuniya, Tokyo, (1972), 335-345.
  • [17] Tanno, S., Infinitesimal isometries on the tangent bundles with complete lift metric, Tensor, N.S., 28 (1974), 139-144.
  • [18] Tanno, S., Killing vectors and geodesic flow vectors on tangent bundle, J. Reine Angew. Math, 238 (1976), 162-171.
  • [19] Walker, A. G., On Ruse’s spaces of recurrent curvature, Proc. Lond. Math. Soc., 52 (1950), 36-64.
  • [20] Yano, K., Integrals Formulas in Riemannian Geometry, Marcel Dekker, Inc. New York, 1970. ara, S., Tangent and cotangent bundles, Marcel Dekker, Inc. New York, 1973.
There are 20 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Stanislaw Ewert-krzemıenıewskı This is me

Publication Date April 30, 2015
Published in Issue Year 2015 Volume: 8 Issue: 1

Cite

APA Ewert-krzemıenıewskı, S. (2015). ON KILLING VECTOR FIELDS ON A TANGENT BUNDLE WITH g-NATURAL METRIC. International Electronic Journal of Geometry, 8(1), 53-76. https://doi.org/10.36890/iejg.592798
AMA Ewert-krzemıenıewskı S. ON KILLING VECTOR FIELDS ON A TANGENT BUNDLE WITH g-NATURAL METRIC. Int. Electron. J. Geom. April 2015;8(1):53-76. doi:10.36890/iejg.592798
Chicago Ewert-krzemıenıewskı, Stanislaw. “ON KILLING VECTOR FIELDS ON A TANGENT BUNDLE WITH G-NATURAL METRIC”. International Electronic Journal of Geometry 8, no. 1 (April 2015): 53-76. https://doi.org/10.36890/iejg.592798.
EndNote Ewert-krzemıenıewskı S (April 1, 2015) ON KILLING VECTOR FIELDS ON A TANGENT BUNDLE WITH g-NATURAL METRIC. International Electronic Journal of Geometry 8 1 53–76.
IEEE S. Ewert-krzemıenıewskı, “ON KILLING VECTOR FIELDS ON A TANGENT BUNDLE WITH g-NATURAL METRIC”, Int. Electron. J. Geom., vol. 8, no. 1, pp. 53–76, 2015, doi: 10.36890/iejg.592798.
ISNAD Ewert-krzemıenıewskı, Stanislaw. “ON KILLING VECTOR FIELDS ON A TANGENT BUNDLE WITH G-NATURAL METRIC”. International Electronic Journal of Geometry 8/1 (April 2015), 53-76. https://doi.org/10.36890/iejg.592798.
JAMA Ewert-krzemıenıewskı S. ON KILLING VECTOR FIELDS ON A TANGENT BUNDLE WITH g-NATURAL METRIC. Int. Electron. J. Geom. 2015;8:53–76.
MLA Ewert-krzemıenıewskı, Stanislaw. “ON KILLING VECTOR FIELDS ON A TANGENT BUNDLE WITH G-NATURAL METRIC”. International Electronic Journal of Geometry, vol. 8, no. 1, 2015, pp. 53-76, doi:10.36890/iejg.592798.
Vancouver Ewert-krzemıenıewskı S. ON KILLING VECTOR FIELDS ON A TANGENT BUNDLE WITH g-NATURAL METRIC. Int. Electron. J. Geom. 2015;8(1):53-76.