Almost complex structures on coframe bundle with Cheeger-Gromoll metric

Year 2022, Volume: 51 Issue: 5, 1260 - 1270, 01.10.2022

Arif Salimov Habil Fattayev

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.

Keywords

Riemannian manifold, coframe bundle, horizontal lift, Cheeger-Gromoll metric, almost complex structure, Nijenhuis tensor

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.