[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
[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.
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.