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Year 2023, Volume: 52 Issue: 2, 303 - 316, 31.03.2023
https://doi.org/10.15672/hujms.1133826

Abstract

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.

Some structures on the coframe bundle with Cheeger-Gromoll metric

Year 2023, Volume: 52 Issue: 2, 303 - 316, 31.03.2023
https://doi.org/10.15672/hujms.1133826

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.
There are 22 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 March 31, 2023
Published in Issue Year 2023 Volume: 52 Issue: 2

Cite

APA Salimov, A., & Fattayev, H. (2023). Some structures on the coframe bundle with Cheeger-Gromoll metric. Hacettepe Journal of Mathematics and Statistics, 52(2), 303-316. https://doi.org/10.15672/hujms.1133826
AMA Salimov A, Fattayev H. Some structures on the coframe bundle with Cheeger-Gromoll metric. Hacettepe Journal of Mathematics and Statistics. March 2023;52(2):303-316. doi:10.15672/hujms.1133826
Chicago Salimov, Arif, and Habil Fattayev. “Some Structures on the Coframe Bundle With Cheeger-Gromoll Metric”. Hacettepe Journal of Mathematics and Statistics 52, no. 2 (March 2023): 303-16. https://doi.org/10.15672/hujms.1133826.
EndNote Salimov A, Fattayev H (March 1, 2023) Some structures on the coframe bundle with Cheeger-Gromoll metric. Hacettepe Journal of Mathematics and Statistics 52 2 303–316.
IEEE A. Salimov and H. Fattayev, “Some structures on the coframe bundle with Cheeger-Gromoll metric”, Hacettepe Journal of Mathematics and Statistics, vol. 52, no. 2, pp. 303–316, 2023, doi: 10.15672/hujms.1133826.
ISNAD Salimov, Arif - Fattayev, Habil. “Some Structures on the Coframe Bundle With Cheeger-Gromoll Metric”. Hacettepe Journal of Mathematics and Statistics 52/2 (March 2023), 303-316. https://doi.org/10.15672/hujms.1133826.
JAMA Salimov A, Fattayev H. Some structures on the coframe bundle with Cheeger-Gromoll metric. Hacettepe Journal of Mathematics and Statistics. 2023;52:303–316.
MLA Salimov, Arif and Habil Fattayev. “Some Structures on the Coframe Bundle With Cheeger-Gromoll Metric”. Hacettepe Journal of Mathematics and Statistics, vol. 52, no. 2, 2023, pp. 303-16, doi:10.15672/hujms.1133826.
Vancouver Salimov A, Fattayev H. Some structures on the coframe bundle with Cheeger-Gromoll metric. Hacettepe Journal of Mathematics and Statistics. 2023;52(2):303-16.