Research Article
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ON THE TANGENT BUNDLE WITH DEFORMED SASAKI METRIC

Year 2013, Volume: 6 Issue: 2, 19 - 31, 30.10.2013

Aydin Gezer

Abstract


Keywords

Almost paracomplex structure deformed Sasaki metric paraholomorphic tensor field pseudo symmetry recurrence

References

  • [1] Abbassi, M. T. K., Note on the classification theorems of g-natural metrics on the tangent bundle of a Riemannian manifold (M, g), Comment. Math. Univ. Carolin., 45 (2004), no. 4, 591-596.
  • [2] Abbassi, M. T. K., Sarih, M., On some hereditary properties of Riemannian g-natural metrics on tangent bundles of Riemannian manifolds, Differential Geom. Appl., 22 (2005), no. 1, 19- 47.
  • [3] Abbassi, M. T. K., Sarih, M., On natural metrics on tangent bundles of Riemannian manifolds, Arch. Math., 41 (2005), 71-92.
  • [4] Binh, T. Q., Tamassy, L., On recurrence or pseudo-symmetry of the Sasakian metric on the tangent bundle of a Riemannian manifold, Indian J. Pure Appl. Math., 35 (2004), no. 4, 555–560.
  • [5] Cartan, E., Sur une classe remarquable d’espaces de Riemannian, Bull. Soc. Math. France, 54 (1926), 214–264.
  • [6] Chaki, M. C., On pseudo-symmetric manifolds, An. Sti. Ale Univ., “AL. I. CUZA” Din Iasi 33 (1987), 53–58.
  • [7] Chaki, M. C., On generalized pseudo-symmetric manifolds, Publ. Math. Debrecen, 45 (1994), 305–312.
  • [8] Cruceanu, V., Fortuny, P., Gadea, P. M., A survey on paracomplex Geometry, Rocky Moun- tain J. Math., 26 (1995), 83-115.
  • [9] Deszcz, R., On pseudosymmetric spaces, Bull. Soc. Math. Belg. Ser. A, 44 (1992), no. 1, 1–34.
  • [10] Dombrowski, P., On the geometry of the tangent bundles, J. Reine and Angew. Math., 210 (1962), 73-88.
  • [11] Fujimoto, A., Theory of G-structures, Publ. Study Group of Geometry, 1, Tokyo Univ., Tokyo, 1972.
  • [12] Gezer, A., Altunbas, M., Some notes concerning Riemannian metrics of Cheeger Gromoll type, J. Math. Anal. Appl., 396 (2012), no. 1, 119–132.
  • [13] Gezer, A., Altunbas, M., Notes on the rescaled Sasaki type metric on the cotangent bundle, Acta Math. Sci. Ser. B Engl. Ed. to appear.
  • [14] Gudmundsson, S., Kappos, E., On the Geometry of the Tangent Bundles, Expo. Math., 20 (2002), 1-41.
  • [15] de Leon, M., Rodrigues, P. R., Methods of Differential Geometry in Analytical Mechanics, North-Holland Mathematics Studies, 1989.
  • [16] Munteanu, M. I., Some aspects on the geometry of the tangent bundles and tangent sphere bundles of a Riemannian manifold, Mediterr. J. Math., 5 (2008), no.1, 43-59.
  • [17] Musso, E., Tricerri, F., Riemannian Metrics on Tangent Bundles, Ann. Mat. Pura. Appl., 150 (1988), no. 4, 1-19.
  • [18] Oproiu, V., Some new geometric structures on the tangent bundle, Publ. Math. Debrecen, 55 (1999), 261-281.
  • [19] Oproiu, V., A locally symmetric Kaehler Einstein structure on the tangent bundle of a space form, Beitr¨age Algebra Geom., 40 (1999), no.2, 363-372.
  • [20] Oproiu, V., A K¨ahler Einstein structure on the tangent bundle of a space form, Int. J. Math. Math. Sci., 25 (2001), no. 3, 183–195.
  • [21] Oproiu, V., Papaghiuc, N., Some classes of almost anti-Hermitian structures on the tangent bundle, Mediterr. J. Math., 1 (2004), no. 3, 269–282.
  • [22] Salimov, A. A., Iscan, M., Etayo, F., Paraholomorphic B-manifold and its properties, Topol- ogy Appl., 154 (2007), no. 4, 925-933.
  • [23] Salimov, A., Gezer, A., Iscan, M., On para-Ka¨hler-Norden structures on the tangent bundles, Ann. Polon. Math. 103 (2012), no. 3, 247–261.
  • [24] S. Sasaki, On the differential geometry of tangent bundles of Riemannian manifolds, Tohoku Math. J., 10 (1958) 338-358.
  • [25] Tachibana, S., Analytic tensor and its generalization, Tohoku Math. J., 12 (1960), no.2, 208-221.
  • [26] Tamassy, L., Binh, T. Q., On weakly symmetric and weakly projective symmetric Riemannian manifolds. Coll. Math. Soc. J. Bolyai, 56 (1989), 663–670.
  • [27] Wang, J., Wang, Y., On the geometry of tangent bundles with the rescaled metric, iv:1104.5584v1
  • [28] Walker, A. G., On Ruses spaces of recurrent curvature, Proc. London Math. Soc., 52 (1950), 36–64.
  • [29] Yano, K., Ako, M., On certain operators associated with tensor field, Kodai Math. Sem. Rep., 20 (1968), 414-436.
  • [30] Yano, K., Ishihara, S., Tangent and Cotangent Bundles, Marcel Dekker, Inc., New York 1973.
  • [31] Zayatuev, B. V., On geometry of tangent Hermtian surface, Webs and Quasigroups. T.S.U. (1995), 139–143.
  • [32] Zayatuev, B. V., On some clases of AH-structures on tangent bundles, Proceedings of the International Conference dedicated to A. Z. Petrov [in Russian], 2000, pp. 53–54.
  • [33] Zayatuev, B. V., On some classes of almost-Hermitian structures on the tangent bundle, Webs and Quasigroups. T.S.U. (2002), 103–106.

Year 2013, Volume: 6 Issue: 2, 19 - 31, 30.10.2013

Aydin Gezer

Abstract

References

  • [1] Abbassi, M. T. K., Note on the classification theorems of g-natural metrics on the tangent bundle of a Riemannian manifold (M, g), Comment. Math. Univ. Carolin., 45 (2004), no. 4, 591-596.
  • [2] Abbassi, M. T. K., Sarih, M., On some hereditary properties of Riemannian g-natural metrics on tangent bundles of Riemannian manifolds, Differential Geom. Appl., 22 (2005), no. 1, 19- 47.
  • [3] Abbassi, M. T. K., Sarih, M., On natural metrics on tangent bundles of Riemannian manifolds, Arch. Math., 41 (2005), 71-92.
  • [4] Binh, T. Q., Tamassy, L., On recurrence or pseudo-symmetry of the Sasakian metric on the tangent bundle of a Riemannian manifold, Indian J. Pure Appl. Math., 35 (2004), no. 4, 555–560.
  • [5] Cartan, E., Sur une classe remarquable d’espaces de Riemannian, Bull. Soc. Math. France, 54 (1926), 214–264.
  • [6] Chaki, M. C., On pseudo-symmetric manifolds, An. Sti. Ale Univ., “AL. I. CUZA” Din Iasi 33 (1987), 53–58.
  • [7] Chaki, M. C., On generalized pseudo-symmetric manifolds, Publ. Math. Debrecen, 45 (1994), 305–312.
  • [8] Cruceanu, V., Fortuny, P., Gadea, P. M., A survey on paracomplex Geometry, Rocky Moun- tain J. Math., 26 (1995), 83-115.
  • [9] Deszcz, R., On pseudosymmetric spaces, Bull. Soc. Math. Belg. Ser. A, 44 (1992), no. 1, 1–34.
  • [10] Dombrowski, P., On the geometry of the tangent bundles, J. Reine and Angew. Math., 210 (1962), 73-88.
  • [11] Fujimoto, A., Theory of G-structures, Publ. Study Group of Geometry, 1, Tokyo Univ., Tokyo, 1972.
  • [12] Gezer, A., Altunbas, M., Some notes concerning Riemannian metrics of Cheeger Gromoll type, J. Math. Anal. Appl., 396 (2012), no. 1, 119–132.
  • [13] Gezer, A., Altunbas, M., Notes on the rescaled Sasaki type metric on the cotangent bundle, Acta Math. Sci. Ser. B Engl. Ed. to appear.
  • [14] Gudmundsson, S., Kappos, E., On the Geometry of the Tangent Bundles, Expo. Math., 20 (2002), 1-41.
  • [15] de Leon, M., Rodrigues, P. R., Methods of Differential Geometry in Analytical Mechanics, North-Holland Mathematics Studies, 1989.
  • [16] Munteanu, M. I., Some aspects on the geometry of the tangent bundles and tangent sphere bundles of a Riemannian manifold, Mediterr. J. Math., 5 (2008), no.1, 43-59.
  • [17] Musso, E., Tricerri, F., Riemannian Metrics on Tangent Bundles, Ann. Mat. Pura. Appl., 150 (1988), no. 4, 1-19.
  • [18] Oproiu, V., Some new geometric structures on the tangent bundle, Publ. Math. Debrecen, 55 (1999), 261-281.
  • [19] Oproiu, V., A locally symmetric Kaehler Einstein structure on the tangent bundle of a space form, Beitr¨age Algebra Geom., 40 (1999), no.2, 363-372.
  • [20] Oproiu, V., A K¨ahler Einstein structure on the tangent bundle of a space form, Int. J. Math. Math. Sci., 25 (2001), no. 3, 183–195.
  • [21] Oproiu, V., Papaghiuc, N., Some classes of almost anti-Hermitian structures on the tangent bundle, Mediterr. J. Math., 1 (2004), no. 3, 269–282.
  • [22] Salimov, A. A., Iscan, M., Etayo, F., Paraholomorphic B-manifold and its properties, Topol- ogy Appl., 154 (2007), no. 4, 925-933.
  • [23] Salimov, A., Gezer, A., Iscan, M., On para-Ka¨hler-Norden structures on the tangent bundles, Ann. Polon. Math. 103 (2012), no. 3, 247–261.
  • [24] S. Sasaki, On the differential geometry of tangent bundles of Riemannian manifolds, Tohoku Math. J., 10 (1958) 338-358.
  • [25] Tachibana, S., Analytic tensor and its generalization, Tohoku Math. J., 12 (1960), no.2, 208-221.
  • [26] Tamassy, L., Binh, T. Q., On weakly symmetric and weakly projective symmetric Riemannian manifolds. Coll. Math. Soc. J. Bolyai, 56 (1989), 663–670.
  • [27] Wang, J., Wang, Y., On the geometry of tangent bundles with the rescaled metric, iv:1104.5584v1
  • [28] Walker, A. G., On Ruses spaces of recurrent curvature, Proc. London Math. Soc., 52 (1950), 36–64.
  • [29] Yano, K., Ako, M., On certain operators associated with tensor field, Kodai Math. Sem. Rep., 20 (1968), 414-436.
  • [30] Yano, K., Ishihara, S., Tangent and Cotangent Bundles, Marcel Dekker, Inc., New York 1973.
  • [31] Zayatuev, B. V., On geometry of tangent Hermtian surface, Webs and Quasigroups. T.S.U. (1995), 139–143.
  • [32] Zayatuev, B. V., On some clases of AH-structures on tangent bundles, Proceedings of the International Conference dedicated to A. Z. Petrov [in Russian], 2000, pp. 53–54.
  • [33] Zayatuev, B. V., On some classes of almost-Hermitian structures on the tangent bundle, Webs and Quasigroups. T.S.U. (2002), 103–106.
There are 33 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Aydin Gezer

Publication Date October 30, 2013
Published in Issue Year 2013 Volume: 6 Issue: 2

Cite

APA Gezer, A. (2013). ON THE TANGENT BUNDLE WITH DEFORMED SASAKI METRIC. International Electronic Journal of Geometry, 6(2), 19-31.
AMA Gezer A. ON THE TANGENT BUNDLE WITH DEFORMED SASAKI METRIC. Int. Electron. J. Geom. October 2013;6(2):19-31.
Chicago Gezer, Aydin. “ON THE TANGENT BUNDLE WITH DEFORMED SASAKI METRIC”. International Electronic Journal of Geometry 6, no. 2 (October 2013): 19-31.
EndNote Gezer A (October 1, 2013) ON THE TANGENT BUNDLE WITH DEFORMED SASAKI METRIC. International Electronic Journal of Geometry 6 2 19–31.
IEEE A. Gezer, “ON THE TANGENT BUNDLE WITH DEFORMED SASAKI METRIC”, Int. Electron. J. Geom., vol. 6, no. 2, pp. 19–31, 2013.
ISNAD Gezer, Aydin. “ON THE TANGENT BUNDLE WITH DEFORMED SASAKI METRIC”. International Electronic Journal of Geometry 6/2 (October 2013), 19-31.
JAMA Gezer A. ON THE TANGENT BUNDLE WITH DEFORMED SASAKI METRIC. Int. Electron. J. Geom. 2013;6:19–31.
MLA Gezer, Aydin. “ON THE TANGENT BUNDLE WITH DEFORMED SASAKI METRIC”. International Electronic Journal of Geometry, vol. 6, no. 2, 2013, pp. 19-31.
Vancouver Gezer A. ON THE TANGENT BUNDLE WITH DEFORMED SASAKI METRIC. Int. Electron. J. Geom. 2013;6(2):19-31.