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

Yıl 2015, Cilt: 8 Sayı: 1, 53 - 76, 30.04.2015
https://doi.org/10.36890/iejg.592798

Öz

  

Kaynakça

  • [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.
Yıl 2015, Cilt: 8 Sayı: 1, 53 - 76, 30.04.2015
https://doi.org/10.36890/iejg.592798

Öz

Kaynakça

  • [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.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Stanislaw Ewert-krzemıenıewskı Bu kişi benim

Yayımlanma Tarihi 30 Nisan 2015
Yayımlandığı Sayı Yıl 2015 Cilt: 8 Sayı: 1

Kaynak Göster

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. Nisan 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, sy. 1 (Nisan 2015): 53-76. https://doi.org/10.36890/iejg.592798.
EndNote Ewert-krzemıenıewskı S (01 Nisan 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., c. 8, sy. 1, ss. 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 (Nisan 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, c. 8, sy. 1, 2015, ss. 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.