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An almost Complex Structure with Norden Metric on the Phase Space

Year 2023, , 412 - 416, 30.04.2023
https://doi.org/10.36890/iejg.1278651

Abstract

On the total space of the cotangent bundle of a Riemannian manifold, we construct a semi-Riemannian metric $G$, with respect to which an almost complex structure $J$ introduced by Oproiu and Poro\cb{s}niuc is self-adjoint. The structure $(J,G)$ turnes out to be an almost complex structure with Norden metric (this notion is known in the literature from Norden's papers). The semi-Riemannian context is different from the Riemannian one, as it is pointed out by Duggal and Bejancu in their monograph. We study this structure and provide some necessary and sufficient conditions for it to be a K\"ahler structure with Norden metric.

References

  • [1] Bejan, C.-L., Nakova, G.: Almost Complex and Hypercomplex Norden Structures Induced by Natural Riemann Extensions. Mathematics. Vol. 10, Issue 15 (2022). 10.3390/math10152625
  • [2] Bejan, C.-L., Nakova, G., Blaga, A.: On Bochner Flat Kähler B-Manifolds. Axioms. 12 (4):336 (2023).
  • [3] Canchev, G., Borisov A.: Note on the almost complex manifolds with a Norden metric. Compt. Rend. Acad. Bulg. Sci. 39 (5), 31-34 (1986)
  • [4] Druta-Romaniuc, S.-L.: Bochner curvature of cotangent bundles with natural diagonal Kähler structures. World Scientific Publishing Company, (2022). https://doi.org/10.1142/978981124810 8 − 0010
  • [5] Duggal, K. L. and Bejancu, A.: Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications. Kluwer Academic, 364, (1996)
  • [6] Norden, A. P.: On a certain class of four-dimensional A-spaces. Izv. Vuzov Mat. 4, 145-157 (1960).
  • [7] Oproiu, V., Poros, niuc, D.D.:A class of Kaehler Einstein structures on the cotangent bundle. Publ. Math. Debrecen. 66, 457-478 (2005).
  • [8] Poroşniuc, D.D.: A class of Kähler Einstein structures on the nonzero cotangent bundle of a space form. Rev. Roumaine Math. Pures Appl. 50,237-252 (2005).
  • [9] Yano, K., Ishihara, S.: Tangent and cotangent bundles. Differential Geometry, M. Dekker, New York (1973).
Year 2023, , 412 - 416, 30.04.2023
https://doi.org/10.36890/iejg.1278651

Abstract

References

  • [1] Bejan, C.-L., Nakova, G.: Almost Complex and Hypercomplex Norden Structures Induced by Natural Riemann Extensions. Mathematics. Vol. 10, Issue 15 (2022). 10.3390/math10152625
  • [2] Bejan, C.-L., Nakova, G., Blaga, A.: On Bochner Flat Kähler B-Manifolds. Axioms. 12 (4):336 (2023).
  • [3] Canchev, G., Borisov A.: Note on the almost complex manifolds with a Norden metric. Compt. Rend. Acad. Bulg. Sci. 39 (5), 31-34 (1986)
  • [4] Druta-Romaniuc, S.-L.: Bochner curvature of cotangent bundles with natural diagonal Kähler structures. World Scientific Publishing Company, (2022). https://doi.org/10.1142/978981124810 8 − 0010
  • [5] Duggal, K. L. and Bejancu, A.: Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications. Kluwer Academic, 364, (1996)
  • [6] Norden, A. P.: On a certain class of four-dimensional A-spaces. Izv. Vuzov Mat. 4, 145-157 (1960).
  • [7] Oproiu, V., Poros, niuc, D.D.:A class of Kaehler Einstein structures on the cotangent bundle. Publ. Math. Debrecen. 66, 457-478 (2005).
  • [8] Poroşniuc, D.D.: A class of Kähler Einstein structures on the nonzero cotangent bundle of a space form. Rev. Roumaine Math. Pures Appl. 50,237-252 (2005).
  • [9] Yano, K., Ishihara, S.: Tangent and cotangent bundles. Differential Geometry, M. Dekker, New York (1973).
There are 9 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Cornelia-livia Bejan 0000-0001-6963-7710

Galia Nakova 0000-0002-1651-8774

Early Pub Date April 27, 2023
Publication Date April 30, 2023
Acceptance Date April 27, 2023
Published in Issue Year 2023

Cite

APA Bejan, C.-l., & Nakova, G. (2023). An almost Complex Structure with Norden Metric on the Phase Space. International Electronic Journal of Geometry, 16(1), 412-416. https://doi.org/10.36890/iejg.1278651
AMA Bejan Cl, Nakova G. An almost Complex Structure with Norden Metric on the Phase Space. Int. Electron. J. Geom. April 2023;16(1):412-416. doi:10.36890/iejg.1278651
Chicago Bejan, Cornelia-livia, and Galia Nakova. “An Almost Complex Structure With Norden Metric on the Phase Space”. International Electronic Journal of Geometry 16, no. 1 (April 2023): 412-16. https://doi.org/10.36890/iejg.1278651.
EndNote Bejan C-l, Nakova G (April 1, 2023) An almost Complex Structure with Norden Metric on the Phase Space. International Electronic Journal of Geometry 16 1 412–416.
IEEE C.-l. Bejan and G. Nakova, “An almost Complex Structure with Norden Metric on the Phase Space”, Int. Electron. J. Geom., vol. 16, no. 1, pp. 412–416, 2023, doi: 10.36890/iejg.1278651.
ISNAD Bejan, Cornelia-livia - Nakova, Galia. “An Almost Complex Structure With Norden Metric on the Phase Space”. International Electronic Journal of Geometry 16/1 (April 2023), 412-416. https://doi.org/10.36890/iejg.1278651.
JAMA Bejan C-l, Nakova G. An almost Complex Structure with Norden Metric on the Phase Space. Int. Electron. J. Geom. 2023;16:412–416.
MLA Bejan, Cornelia-livia and Galia Nakova. “An Almost Complex Structure With Norden Metric on the Phase Space”. International Electronic Journal of Geometry, vol. 16, no. 1, 2023, pp. 412-6, doi:10.36890/iejg.1278651.
Vancouver Bejan C-l, Nakova G. An almost Complex Structure with Norden Metric on the Phase Space. Int. Electron. J. Geom. 2023;16(1):412-6.