Year 2023,
Volume: 52 Issue: 2, 303 - 316, 31.03.2023
Arif Salimov
,
Habil Fattayev
References
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the tangent bundle, Mediterr. J. Math. 1 (3), 269-282, 2004.
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Anal. 6, 225-248, 1948.
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bundles, Ann. Polon. Math. 103 (3), 247-261, 2012.
- [16] A. Salimov and H. Fattayev, Lifts of derivations in the coframe bundle, Mediterr. J.
Math. 17 (48), 1-12, 2020.
- [17] A. Salimov, M. Iscan and F. Etayo, Paraholomorphic B-manifolds and its properties,
Topology Appl. 154 , 425-433, 2007.
- [18] S. Sasaki, On the differential geometry of tangent bundles of Riemannian manifolds,
Tohoku Math. J. 10 , 338-358, 1958.
- [19] M. Sekizawa, Curvatures of tangent bundles with Cheeger-Gromoll metric, Tokyo J.
Math. 14 (2), 407-417, 1991.
- [20] A. Trautman, The geometry of gauge fields, Czech J. Phys. 29, 107-116, 1979.
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Some structures on the coframe bundle with Cheeger-Gromoll metric
Year 2023,
Volume: 52 Issue: 2, 303 - 316, 31.03.2023
Arif Salimov
,
Habil Fattayev
Abstract
In this paper an almost paracomplex structures on the coframe bundle with Cheeger- Gromoll metric are defined and later we obtained the integrability conditions of these structures. Also we proved that para-Norden structures which exists on coframe bundle are non-Kahler-Norden.
References
- [1] C-L. Bejan, The existence problem of hyberbolic structures on vector bundles, Publ.
Inst. Math. (N.S.) 53 (67), 133-138, 1993.
- [2] L. Boi, Geometrical and topological foundations of theoretical physics: from gauge
theories to string proqram, IJMMS 34, 1774-1830, 2004.
- [3] J. Cheeger and D. Gromoll, On the structure of complete manifolds of nonnegative
curvature, Ann. of Math. 96, 413-443, 1972.
- [4] V. Cruceany, P. Fortuny and P.M. Gadea, A survey on Paracomplex Geometry, Rocky
Mountain J. Math. 26 (1), 133-138, 1993.
- [5] S.L. S.L. Druţˇa-Romaniuc, Classes of general natural anti-Hermitian structures on the
cotangent bundles, Mediterr. J. Math. 8 (2), 161-179, 2011.
- [6] P.M. Gadea and A.M. Amilibia, Spaces of constant paraholomorphic sectional curvature,
Pacific J. Math. 136, 85-101, 1989.
- [7] Z. Hou and L. Sun, Geometry of tangent bundle with Cheeger-Gromoll type metric,
J. Math. Anal. Appl. 402, 493-504, 2013.
- [8] M. Iscan and A. Salimov, On Kahler-Norden manifolds, Proc. Indian Acad. Sci. Math.
Sci.119, 71-80, 2009.
- [9] S. Kaneyuki and M. Kozai, Paracomplex structures and affine symmetric spaces,
Tokyo J. Math. 8, 81-98, 1985.
- [10] P. Libermann, Sur les structures presque paracomplexes, C.R. Acad. Sci. Paris, Ser. I
Math. 234, 2517-2519, 1952.
- [11] E. Musso, F. Tricerri, Riemannian metrics on tangent bundles, Ann. Math. Pura.
Appl. 150 (4), 1-20, 1988.
- [12] M. Nakahara, Geometry, topology and physics, (Adam Hilger, Bristol, 1990.
- [13] V. Oproiu and N. Papaghiuc, Some classes of almost anti-Hermitian structures on
the tangent bundle, Mediterr. J. Math. 1 (3), 269-282, 2004.
- [14] P.K. Rashevskii, The scalar field in a stratified space, Trudy Sem. Vektor. Tenzor.
Anal. 6, 225-248, 1948.
- [15] A. Salimov, A. Gezer and M. Iscan, On para-Kahler-Norden structures on the tangent
bundles, Ann. Polon. Math. 103 (3), 247-261, 2012.
- [16] A. Salimov and H. Fattayev, Lifts of derivations in the coframe bundle, Mediterr. J.
Math. 17 (48), 1-12, 2020.
- [17] A. Salimov, M. Iscan and F. Etayo, Paraholomorphic B-manifolds and its properties,
Topology Appl. 154 , 425-433, 2007.
- [18] S. Sasaki, On the differential geometry of tangent bundles of Riemannian manifolds,
Tohoku Math. J. 10 , 338-358, 1958.
- [19] M. Sekizawa, Curvatures of tangent bundles with Cheeger-Gromoll metric, Tokyo J.
Math. 14 (2), 407-417, 1991.
- [20] A. Trautman, The geometry of gauge fields, Czech J. Phys. 29, 107-116, 1979.
- [21] V.V. Vishnevskii, A.P. Shirokov and V.V. Shurygin, Spaces over algebras, Kazan.
Gos. Univ., Kazan, 1985, (Russian).
- [22] V.V. Vishnevskii, Integrable affinor structures and their plural interpretations, J.
Math. Sci. 108, 151-187, 2002.