Research Article
BibTex RIS Cite

CURVATURE PROPERTIES OF RIEMANNIAN METRICS OF THE FORM Sgf +H g ON THE TANGENT BUNDLE OVER A RIEMANNIAN MANIFOLD (M,g)

Year 2015, , 181 - 194, 30.10.2015

Aydin Gezer , Lokman Bilen , Cağri Karaman Murat Altunbaş

https://doi.org/10.36890/iejg.592306
Cited By: 2

Abstract


Keywords

Metric connection Riemannian metric Riemannian curvature tensor tangent bundle Weyl curvature tensor

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, no. 4, 591- 596(2004).
  • [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 no. 1, 19-47 (2005).
  • [3] Abbassi, M. T. K., Sarih, M.: On natural metrics on tangent bundles of Riemannian manifolds. Arch. Math., 41, 71-92 (2005).
  • [4] Dombrowski, P.: On the geometry of the tangent bundles. J. reine and angew. Math. 210, 73-88 (1962).
  • [5] Gezer, A., On the tangent bundle with deformed Sasaki metric. Int. Electron. J. Geom. 6, no. 2, 19–31, (2013).
  • [6] Gezer, A., Altunbas, M.: Notes on the rescaled Sasaki type metric on the cotangent bundle, Acta Math. Sci. Ser. B Engl. Ed. 34 (2014), no. 1, 162–174.
  • [7] Gezer, A., Tarakci, O., Salimov A. A.: On the geometry of tangent bundles with the metric II + III. Ann. Polon. Math. 97, no. 1, 73–85 (2010).
  • [8] Hayden, H. A.:Sub-spaces of a space with torsion. Proc. London Math. Soc. S2-34, 27-50 (1932).
  • [9] Kolar, I., Michor, P. W., Slovak, J.: Natural operations in differential geometry. Springer- Verlang, Berlin, 1993.
  • [10] Kowalski, O.: Curvature of the Induced Riemannian Metric on the Tangent Bundle of a Riemannian Manifold. J. Reine Angew. Math. 250, 124-129 (1971).
  • [11] Kowalski, O., Sekizawa, M.: Natural transformation of Riemannian metrics on manifolds to metrics on tangent bundles-a classification. Bull. Tokyo Gakugei Univ. 40 no. 4, 1-29 (1988).
  • [12] Musso, E., Tricerri, F.: Riemannian Metrics on Tangent Bundles. Ann. Mat. Pura. Appl. 150, no. 4, 1-19 (1988).
  • [13] Oproiu, V., Papaghiuc, N.: An anti-K¨ahlerian Einstein structure on the tangent bundle of a space form. Colloq. Math. 103, no. 1, 41–46 (2005).
  • [14] Oproiu, V., Papaghiuc, N.: Einstein quasi-anti-Hermitian structures on the tangent bundle. An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 50, no. 2, 347–360 (2004).
  • [15] Oproiu, V., Papaghiuc, N.: Classes of almost anti-Hermitian structures on the tangent bundle of a Riemannian manifold. An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 50, no. 1, 175–190 (2004).
  • [16] Oproiu, V., Papaghiuc, N.: Some classes of almost anti-Hermitian structures on the tangent bundle. Mediterr. J. Math. 1 , no. 3, 269–282 (2004).
  • [17] Sasaki, S.: On the differential geometry of tangent bundles of Riemannian manifolds. Tohoku Math. J. 10, 338-358 (1958).
  • [18] Wang, J., Wang, Y.: On the geometry of tangent bundles with the rescaled metric.arXiv:1104.5584v1
  • [19] Yano, K., Ishihara, S.: Tangent and Cotangent Bundles. Marcel Dekker, Inc., New York 1973.
  • [20] Zayatuev, B. V.: On geometry of tangent Hermtian surface. Webs and Quasigroups. T.S.U. 139–143 (1995).
  • [21] Zayatuev, B. V.: On some clases of AH-structures on tangent bundles. Proceedings of the International Conference dedicated to A. Z. Petrov [in Russian], pp. 53–54 (2000).
  • [22] Zayatuev, B. V.: On some classes of almost-Hermitian structures on the tangent bundle. Webs and Quasigroups T.S.U. 103–106(2002).

Year 2015, , 181 - 194, 30.10.2015

Aydin Gezer , Lokman Bilen , Cağri Karaman Murat Altunbaş

https://doi.org/10.36890/iejg.592306
Cited By: 2

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, no. 4, 591- 596(2004).
  • [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 no. 1, 19-47 (2005).
  • [3] Abbassi, M. T. K., Sarih, M.: On natural metrics on tangent bundles of Riemannian manifolds. Arch. Math., 41, 71-92 (2005).
  • [4] Dombrowski, P.: On the geometry of the tangent bundles. J. reine and angew. Math. 210, 73-88 (1962).
  • [5] Gezer, A., On the tangent bundle with deformed Sasaki metric. Int. Electron. J. Geom. 6, no. 2, 19–31, (2013).
  • [6] Gezer, A., Altunbas, M.: Notes on the rescaled Sasaki type metric on the cotangent bundle, Acta Math. Sci. Ser. B Engl. Ed. 34 (2014), no. 1, 162–174.
  • [7] Gezer, A., Tarakci, O., Salimov A. A.: On the geometry of tangent bundles with the metric II + III. Ann. Polon. Math. 97, no. 1, 73–85 (2010).
  • [8] Hayden, H. A.:Sub-spaces of a space with torsion. Proc. London Math. Soc. S2-34, 27-50 (1932).
  • [9] Kolar, I., Michor, P. W., Slovak, J.: Natural operations in differential geometry. Springer- Verlang, Berlin, 1993.
  • [10] Kowalski, O.: Curvature of the Induced Riemannian Metric on the Tangent Bundle of a Riemannian Manifold. J. Reine Angew. Math. 250, 124-129 (1971).
  • [11] Kowalski, O., Sekizawa, M.: Natural transformation of Riemannian metrics on manifolds to metrics on tangent bundles-a classification. Bull. Tokyo Gakugei Univ. 40 no. 4, 1-29 (1988).
  • [12] Musso, E., Tricerri, F.: Riemannian Metrics on Tangent Bundles. Ann. Mat. Pura. Appl. 150, no. 4, 1-19 (1988).
  • [13] Oproiu, V., Papaghiuc, N.: An anti-K¨ahlerian Einstein structure on the tangent bundle of a space form. Colloq. Math. 103, no. 1, 41–46 (2005).
  • [14] Oproiu, V., Papaghiuc, N.: Einstein quasi-anti-Hermitian structures on the tangent bundle. An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 50, no. 2, 347–360 (2004).
  • [15] Oproiu, V., Papaghiuc, N.: Classes of almost anti-Hermitian structures on the tangent bundle of a Riemannian manifold. An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 50, no. 1, 175–190 (2004).
  • [16] Oproiu, V., Papaghiuc, N.: Some classes of almost anti-Hermitian structures on the tangent bundle. Mediterr. J. Math. 1 , no. 3, 269–282 (2004).
  • [17] Sasaki, S.: On the differential geometry of tangent bundles of Riemannian manifolds. Tohoku Math. J. 10, 338-358 (1958).
  • [18] Wang, J., Wang, Y.: On the geometry of tangent bundles with the rescaled metric.arXiv:1104.5584v1
  • [19] Yano, K., Ishihara, S.: Tangent and Cotangent Bundles. Marcel Dekker, Inc., New York 1973.
  • [20] Zayatuev, B. V.: On geometry of tangent Hermtian surface. Webs and Quasigroups. T.S.U. 139–143 (1995).
  • [21] Zayatuev, B. V.: On some clases of AH-structures on tangent bundles. Proceedings of the International Conference dedicated to A. Z. Petrov [in Russian], pp. 53–54 (2000).
  • [22] Zayatuev, B. V.: On some classes of almost-Hermitian structures on the tangent bundle. Webs and Quasigroups T.S.U. 103–106(2002).
There are 22 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Aydin Gezer

Lokman Bilen

Cağri Karaman This is me

Murat Altunbaş

Publication Date October 30, 2015
Published in Issue Year 2015

Cite

APA Gezer, A., Bilen, L., Karaman, C., Altunbaş, M. (2015). CURVATURE PROPERTIES OF RIEMANNIAN METRICS OF THE FORM Sgf +H g ON THE TANGENT BUNDLE OVER A RIEMANNIAN MANIFOLD (M,g). International Electronic Journal of Geometry, 8(2), 181-194. https://doi.org/10.36890/iejg.592306
AMA Gezer A, Bilen L, Karaman C, Altunbaş M. CURVATURE PROPERTIES OF RIEMANNIAN METRICS OF THE FORM Sgf +H g ON THE TANGENT BUNDLE OVER A RIEMANNIAN MANIFOLD (M,g). Int. Electron. J. Geom. October 2015;8(2):181-194. doi:10.36890/iejg.592306
Chicago Gezer, Aydin, Lokman Bilen, Cağri Karaman, and Murat Altunbaş. “CURVATURE PROPERTIES OF RIEMANNIAN METRICS OF THE FORM Sgf +H G ON THE TANGENT BUNDLE OVER A RIEMANNIAN MANIFOLD (M,g)”. International Electronic Journal of Geometry 8, no. 2 (October 2015): 181-94. https://doi.org/10.36890/iejg.592306.
EndNote Gezer A, Bilen L, Karaman C, Altunbaş M (October 1, 2015) CURVATURE PROPERTIES OF RIEMANNIAN METRICS OF THE FORM Sgf +H g ON THE TANGENT BUNDLE OVER A RIEMANNIAN MANIFOLD (M,g). International Electronic Journal of Geometry 8 2 181–194.
IEEE A. Gezer, L. Bilen, C. Karaman, and M. Altunbaş, “CURVATURE PROPERTIES OF RIEMANNIAN METRICS OF THE FORM Sgf +H g ON THE TANGENT BUNDLE OVER A RIEMANNIAN MANIFOLD (M,g)”, Int. Electron. J. Geom., vol. 8, no. 2, pp. 181–194, 2015, doi: 10.36890/iejg.592306.
ISNAD Gezer, Aydin et al. “CURVATURE PROPERTIES OF RIEMANNIAN METRICS OF THE FORM Sgf +H G ON THE TANGENT BUNDLE OVER A RIEMANNIAN MANIFOLD (M,g)”. International Electronic Journal of Geometry 8/2 (October 2015), 181-194. https://doi.org/10.36890/iejg.592306.
JAMA Gezer A, Bilen L, Karaman C, Altunbaş M. CURVATURE PROPERTIES OF RIEMANNIAN METRICS OF THE FORM Sgf +H g ON THE TANGENT BUNDLE OVER A RIEMANNIAN MANIFOLD (M,g). Int. Electron. J. Geom. 2015;8:181–194.
MLA Gezer, Aydin et al. “CURVATURE PROPERTIES OF RIEMANNIAN METRICS OF THE FORM Sgf +H G ON THE TANGENT BUNDLE OVER A RIEMANNIAN MANIFOLD (M,g)”. International Electronic Journal of Geometry, vol. 8, no. 2, 2015, pp. 181-94, doi:10.36890/iejg.592306.
Vancouver Gezer A, Bilen L, Karaman C, Altunbaş M. CURVATURE PROPERTIES OF RIEMANNIAN METRICS OF THE FORM Sgf +H g ON THE TANGENT BUNDLE OVER A RIEMANNIAN MANIFOLD (M,g). Int. Electron. J. Geom. 2015;8(2):181-94.

Cited By

Some Almost $B$-Structures on the Tangent Bundle Equipped with a Vertical Rescaled Metric
Turkish Journal of Mathematics and Computer Science
https://doi.org/10.47000/tjmcs.1458966
Statistical structures and Killing vector fields on tangent bundles with respect to two different metrics
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics
https://doi.org/10.31801/cfsuasmas.1160135