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Almost complex structures on coframe bundle with Cheeger-Gromoll metric

Year 2022, Volume: 51 Issue: 5, 1260 - 1270, 01.10.2022
https://doi.org/10.15672/hujms.1012725

Abstract

In this paper we introduce several almost complex structures compatible with Cheeger-Gromoll metric on the coframe bundle and investigate their integrability conditions.

References

  • [1] F. Agca and A. Salimov, Some notes concerning Cheeger-Gromoll metrics, Hacet. J. Math. Stat. 42(5), 533-549, 2013.
  • [2] C.L. Bejan and S.L. Druţˇa-Romaniuc, Harmonic almost complex structures with respect to general natural metrics, Mediterr. J. Math. 11(1), 123-136, 2013.
  • [3] J. Cheeger and D. Gromoll, On the structure of complete manifolds of nonnegative curvature, Ann. Math. 96, 413-443, 1972.
  • [4] S.L. Druţa-Romaniuc, Cotangent bundles with general natural Kahler structures, Rev. Roumaine Math. Pures Appl. 54(1), 13-23, 2009.
  • [5] H. Fattayev and A. Salimov, Diagonal lifts of metrics to coframe bundle, Proc. IMM NAS Azerbaijan 44(2), 328-337, 2018.
  • [6] S. Gudmondson and E. Kappos, On the geometry of the tangent bundles, Expo. Math. 20(1), 1-41, 2002.
  • [7] Z. Hou and L. Sun, Geometry of tangent bundle with Cheeger-Gromoll type metric, J. Math. Anal. Appl. 402, 493-504, 2013.
  • [8] O. Kowalski, Curvatures of the induced Riemannian metric of the tangent bundle of Riemannian manifold, J. Reine Angew. Math. 250, 124-129, 1971
  • [9] M. Munteanu, Cheeger-Gromoll type metrics on the tangent bundle, Sci. Ann. Univ. Agric. Sci. Vet. Med. 49(2), 257-268, 2006.
  • [10] E. Musso and F. Tricerri, Riemannian metrics on tangent bundles, Ann. Math. Pura. Appl. 150 (4), 1-20, 1988.
  • [11] V. Oproiu and D. Poroşniuc, A Kahler Einstein structure on the cotangent bundle of a Riemannian manifold, An. Şhtiint. Univ. Al. I. Cuza, Iaşi 49, s. I, Mathematics f.2, 399-414, 2003.
  • [12] A. Salimov and H. Fattayev, Lifts of derivations in the coframe bundle, Mediterr. J. Math. 17(48), 1-12, 2020.
  • [13] S. Sasaki, On the differential geometry of the tangent bundle of Riemannian manifolds, Tohoku Math. J. 10, 238-254, 1958.
  • [14] M. Sekizawa, Curvatures of tangent bundles with Cheeger-Gromoll metric, Tokyo J. Math. 14(2), 407-417, 1991.
  • [15] M. Tahara, L. Vanhecke and Y. Watanabe, New structures on tangent bundles, Note Mat. 18(1), 131-141, 1998.
  • [16] K. Yano and S. Ishihara, Tangent and cotangent bundles, Marsel Dekker Inc., New York, 1973.
Year 2022, Volume: 51 Issue: 5, 1260 - 1270, 01.10.2022
https://doi.org/10.15672/hujms.1012725

Abstract

References

  • [1] F. Agca and A. Salimov, Some notes concerning Cheeger-Gromoll metrics, Hacet. J. Math. Stat. 42(5), 533-549, 2013.
  • [2] C.L. Bejan and S.L. Druţˇa-Romaniuc, Harmonic almost complex structures with respect to general natural metrics, Mediterr. J. Math. 11(1), 123-136, 2013.
  • [3] J. Cheeger and D. Gromoll, On the structure of complete manifolds of nonnegative curvature, Ann. Math. 96, 413-443, 1972.
  • [4] S.L. Druţa-Romaniuc, Cotangent bundles with general natural Kahler structures, Rev. Roumaine Math. Pures Appl. 54(1), 13-23, 2009.
  • [5] H. Fattayev and A. Salimov, Diagonal lifts of metrics to coframe bundle, Proc. IMM NAS Azerbaijan 44(2), 328-337, 2018.
  • [6] S. Gudmondson and E. Kappos, On the geometry of the tangent bundles, Expo. Math. 20(1), 1-41, 2002.
  • [7] Z. Hou and L. Sun, Geometry of tangent bundle with Cheeger-Gromoll type metric, J. Math. Anal. Appl. 402, 493-504, 2013.
  • [8] O. Kowalski, Curvatures of the induced Riemannian metric of the tangent bundle of Riemannian manifold, J. Reine Angew. Math. 250, 124-129, 1971
  • [9] M. Munteanu, Cheeger-Gromoll type metrics on the tangent bundle, Sci. Ann. Univ. Agric. Sci. Vet. Med. 49(2), 257-268, 2006.
  • [10] E. Musso and F. Tricerri, Riemannian metrics on tangent bundles, Ann. Math. Pura. Appl. 150 (4), 1-20, 1988.
  • [11] V. Oproiu and D. Poroşniuc, A Kahler Einstein structure on the cotangent bundle of a Riemannian manifold, An. Şhtiint. Univ. Al. I. Cuza, Iaşi 49, s. I, Mathematics f.2, 399-414, 2003.
  • [12] A. Salimov and H. Fattayev, Lifts of derivations in the coframe bundle, Mediterr. J. Math. 17(48), 1-12, 2020.
  • [13] S. Sasaki, On the differential geometry of the tangent bundle of Riemannian manifolds, Tohoku Math. J. 10, 238-254, 1958.
  • [14] M. Sekizawa, Curvatures of tangent bundles with Cheeger-Gromoll metric, Tokyo J. Math. 14(2), 407-417, 1991.
  • [15] M. Tahara, L. Vanhecke and Y. Watanabe, New structures on tangent bundles, Note Mat. 18(1), 131-141, 1998.
  • [16] K. Yano and S. Ishihara, Tangent and cotangent bundles, Marsel Dekker Inc., New York, 1973.
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Arif Salimov 0000-0002-4171-3379

Habil Fattayev 0000-0003-0861-3904

Publication Date October 1, 2022
Published in Issue Year 2022 Volume: 51 Issue: 5

Cite

APA Salimov, A., & Fattayev, H. (2022). Almost complex structures on coframe bundle with Cheeger-Gromoll metric. Hacettepe Journal of Mathematics and Statistics, 51(5), 1260-1270. https://doi.org/10.15672/hujms.1012725
AMA Salimov A, Fattayev H. Almost complex structures on coframe bundle with Cheeger-Gromoll metric. Hacettepe Journal of Mathematics and Statistics. October 2022;51(5):1260-1270. doi:10.15672/hujms.1012725
Chicago Salimov, Arif, and Habil Fattayev. “Almost Complex Structures on Coframe Bundle With Cheeger-Gromoll Metric”. Hacettepe Journal of Mathematics and Statistics 51, no. 5 (October 2022): 1260-70. https://doi.org/10.15672/hujms.1012725.
EndNote Salimov A, Fattayev H (October 1, 2022) Almost complex structures on coframe bundle with Cheeger-Gromoll metric. Hacettepe Journal of Mathematics and Statistics 51 5 1260–1270.
IEEE A. Salimov and H. Fattayev, “Almost complex structures on coframe bundle with Cheeger-Gromoll metric”, Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 5, pp. 1260–1270, 2022, doi: 10.15672/hujms.1012725.
ISNAD Salimov, Arif - Fattayev, Habil. “Almost Complex Structures on Coframe Bundle With Cheeger-Gromoll Metric”. Hacettepe Journal of Mathematics and Statistics 51/5 (October 2022), 1260-1270. https://doi.org/10.15672/hujms.1012725.
JAMA Salimov A, Fattayev H. Almost complex structures on coframe bundle with Cheeger-Gromoll metric. Hacettepe Journal of Mathematics and Statistics. 2022;51:1260–1270.
MLA Salimov, Arif and Habil Fattayev. “Almost Complex Structures on Coframe Bundle With Cheeger-Gromoll Metric”. Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 5, 2022, pp. 1260-7, doi:10.15672/hujms.1012725.
Vancouver Salimov A, Fattayev H. Almost complex structures on coframe bundle with Cheeger-Gromoll metric. Hacettepe Journal of Mathematics and Statistics. 2022;51(5):1260-7.