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F-Planar Curves on para-Kähler Manifolds

Year 2024, , 119 - 125, 30.06.2024
https://doi.org/10.47000/tjmcs.1295830

Abstract

This paper deals with classifications of F-planar curves on para-K\"{a}hler
manifolds. Also, we give some examples related to them.

References

  • Adachi, T., K¨ahler magnetic fields on a complex projective space, Proc. Japan Acad., 70(1994), 12–13.
  • Cabrerizo, J.L., Fernandez, M., G´omez, J.S., The contact magnetic flow in 3D Sasakian manifolds, J. Phys. A. Math. Theor., 42(2009), 195201.
  • Cortes, V., Lawn, M.A., Sch¨afer, L., Affine hyperspheres associated to special para-K¨ahler manifolds, Int. J. Geom. Methods, 3(2006), 995–1009.
  • Cortes, V., The special geometry of Euclidean supersymmetry: a survey, Rev. Union Mat. Argent, 47(2006), 29–34.
  • Defever, F., Verstraelen, L., Deszcz, R., On pseudosymmetric para-K¨ahler manifolds, In Colloquium Mathematicae, 74(1998), 253–260.
  • Druta-Romaniuc, S.L., Munteanu, M.I., Magnetic curves corresponding to Killing magnetic fields in E3, J. Math. Phys., 52(2011), 113506.
  • Gezer, A., Aktas, B., Durmaz, O., Notes concerning K¨ahler and anti-K¨ahler structures on quasi-statistical manifolds, arXiv preprint arXiv, (2023), 2307.15065.
  • Hinterleitner, I., Mikes, J., On F-planar mappings of spaces with affine connections, Note di Matematica, 27(1)(2009), 111-118.
  • Jleli, M., Munteanu, M.I., Magnetic curves on flat para-K¨ahler manifolds, Turkish Journal of Mathematics, 39(2015), 963–969.
  • Keçilioğlu, O., Gündoğan, H., Pseudo matrix multiplication, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 66(2017), 37–43.
  • Libermann, P., Sur le probl`eme d´equivalence de certains structures infinit´esimales, Ann. Mat. Pura App., 36(1954), 27120.
  • Munteanu, M.I., Magnetic curves in the Euclidean space: one example, several approaches, Publ. I Math-Beograd, 94(2013), 141–150.
  • Nistor, A.I., New examples of F-planar curves in 3-dimensional warped product manifolds, Kragujevac J. Math., 43(2019), 247–257.
  • Noyan, E.B., Gündüzalp, Y., Proper semi-slant pseudo-Riemannian submersions in para-Kaehler geometry, International Electronic Journal of Geometry, 15(2022), 253–265.
  • Noyan, E.B., Gunduzalp, Y., Proper bi-slant pseudo-Riemannian submersions whose total manifolds are para-Kaehler manifolds, Honam Math. J., 44(2022), 370–383.
  • Rashevski, P.K., The scalar field in a stratified space, Trudy Sem Vektor Tenzor Anal., 6(1948), 225–248.
  • Rozenfeld, B.A., On unitary and stratified spaces, Trudy Sem Vektor Tenzor Anal., 7(1949), 260–275.
  • Ruse, H.S., On parallel fields of planes in a Riemannian manifold, Quart J. Math. Oxford Ser., 20(1949), 218–234.
  • Vaisman, I., Generalized para-K¨ahler manifolds, Differential Geometry and Its Applications, 42(2015), 84–103
Year 2024, , 119 - 125, 30.06.2024
https://doi.org/10.47000/tjmcs.1295830

Abstract

References

  • Adachi, T., K¨ahler magnetic fields on a complex projective space, Proc. Japan Acad., 70(1994), 12–13.
  • Cabrerizo, J.L., Fernandez, M., G´omez, J.S., The contact magnetic flow in 3D Sasakian manifolds, J. Phys. A. Math. Theor., 42(2009), 195201.
  • Cortes, V., Lawn, M.A., Sch¨afer, L., Affine hyperspheres associated to special para-K¨ahler manifolds, Int. J. Geom. Methods, 3(2006), 995–1009.
  • Cortes, V., The special geometry of Euclidean supersymmetry: a survey, Rev. Union Mat. Argent, 47(2006), 29–34.
  • Defever, F., Verstraelen, L., Deszcz, R., On pseudosymmetric para-K¨ahler manifolds, In Colloquium Mathematicae, 74(1998), 253–260.
  • Druta-Romaniuc, S.L., Munteanu, M.I., Magnetic curves corresponding to Killing magnetic fields in E3, J. Math. Phys., 52(2011), 113506.
  • Gezer, A., Aktas, B., Durmaz, O., Notes concerning K¨ahler and anti-K¨ahler structures on quasi-statistical manifolds, arXiv preprint arXiv, (2023), 2307.15065.
  • Hinterleitner, I., Mikes, J., On F-planar mappings of spaces with affine connections, Note di Matematica, 27(1)(2009), 111-118.
  • Jleli, M., Munteanu, M.I., Magnetic curves on flat para-K¨ahler manifolds, Turkish Journal of Mathematics, 39(2015), 963–969.
  • Keçilioğlu, O., Gündoğan, H., Pseudo matrix multiplication, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 66(2017), 37–43.
  • Libermann, P., Sur le probl`eme d´equivalence de certains structures infinit´esimales, Ann. Mat. Pura App., 36(1954), 27120.
  • Munteanu, M.I., Magnetic curves in the Euclidean space: one example, several approaches, Publ. I Math-Beograd, 94(2013), 141–150.
  • Nistor, A.I., New examples of F-planar curves in 3-dimensional warped product manifolds, Kragujevac J. Math., 43(2019), 247–257.
  • Noyan, E.B., Gündüzalp, Y., Proper semi-slant pseudo-Riemannian submersions in para-Kaehler geometry, International Electronic Journal of Geometry, 15(2022), 253–265.
  • Noyan, E.B., Gunduzalp, Y., Proper bi-slant pseudo-Riemannian submersions whose total manifolds are para-Kaehler manifolds, Honam Math. J., 44(2022), 370–383.
  • Rashevski, P.K., The scalar field in a stratified space, Trudy Sem Vektor Tenzor Anal., 6(1948), 225–248.
  • Rozenfeld, B.A., On unitary and stratified spaces, Trudy Sem Vektor Tenzor Anal., 7(1949), 260–275.
  • Ruse, H.S., On parallel fields of planes in a Riemannian manifold, Quart J. Math. Oxford Ser., 20(1949), 218–234.
  • Vaisman, I., Generalized para-K¨ahler manifolds, Differential Geometry and Its Applications, 42(2015), 84–103
There are 19 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Atilla Karabacak 0000-0002-6170-3709

Ömer Tarakcı 0000-0003-0302-7156

Publication Date June 30, 2024
Published in Issue Year 2024

Cite

APA Karabacak, A., & Tarakcı, Ö. (2024). F-Planar Curves on para-Kähler Manifolds. Turkish Journal of Mathematics and Computer Science, 16(1), 119-125. https://doi.org/10.47000/tjmcs.1295830
AMA Karabacak A, Tarakcı Ö. F-Planar Curves on para-Kähler Manifolds. TJMCS. June 2024;16(1):119-125. doi:10.47000/tjmcs.1295830
Chicago Karabacak, Atilla, and Ömer Tarakcı. “F-Planar Curves on Para-Kähler Manifolds”. Turkish Journal of Mathematics and Computer Science 16, no. 1 (June 2024): 119-25. https://doi.org/10.47000/tjmcs.1295830.
EndNote Karabacak A, Tarakcı Ö (June 1, 2024) F-Planar Curves on para-Kähler Manifolds. Turkish Journal of Mathematics and Computer Science 16 1 119–125.
IEEE A. Karabacak and Ö. Tarakcı, “F-Planar Curves on para-Kähler Manifolds”, TJMCS, vol. 16, no. 1, pp. 119–125, 2024, doi: 10.47000/tjmcs.1295830.
ISNAD Karabacak, Atilla - Tarakcı, Ömer. “F-Planar Curves on Para-Kähler Manifolds”. Turkish Journal of Mathematics and Computer Science 16/1 (June 2024), 119-125. https://doi.org/10.47000/tjmcs.1295830.
JAMA Karabacak A, Tarakcı Ö. F-Planar Curves on para-Kähler Manifolds. TJMCS. 2024;16:119–125.
MLA Karabacak, Atilla and Ömer Tarakcı. “F-Planar Curves on Para-Kähler Manifolds”. Turkish Journal of Mathematics and Computer Science, vol. 16, no. 1, 2024, pp. 119-25, doi:10.47000/tjmcs.1295830.
Vancouver Karabacak A, Tarakcı Ö. F-Planar Curves on para-Kähler Manifolds. TJMCS. 2024;16(1):119-25.