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DOI :10.26650/ijmath.2023.00003   IUP :10.26650/ijmath.2023.00003    Full Text (PDF)

Clairaut and Einstein conditions for locally conformal Kaehler submersions

Beran Pirinççi, Çağrıhan Çimen, Deniz Ulusoy

In the present paper, we study Clairaut submersions and Einstein conditions whose total manifolds are locally conformal Kaehler manifolds. We first give a necessary and sufficient condition for a curve to be geodesic on total manifold of a locally conformal Kaehler submersion. Then, we investigate conditions for a locally conformal Kaehler submersion to be a Clairaut submersion.We find the Ricci and scalar curvature formulas between any fiber of the total manifold and the base manifold of a locally conformal Kaehler submersion and give necessary and sufficient conditions for the total manifold of a locally conformal Kaehler submersion to be Einstein. Finally, we obtain some formulas for sectional and holomorphic sectional curvatures for a locally conformal Kaehler submersion.

Keywords: Riemannian submersion, almost Hermitian submersion, locally conformal Kaehler submersion, Clairaut submersion, Einstein manifold.

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References

  • Allison, D., 1996, Lorentzian Clairaut submersions, Geom. Dedicata, 63(3), 309-319. google scholar
  • Bishop, R.L., 1972, Clairaut submersions, differential geometry (in Honor of Kentaro Yano), Tokyo, Kinokuniya, 21-31. google scholar
  • Çimen Ç., Pirinççi B., Taştan H.M., Ulusoy D., 2023, On locally conformal Kaehler submersions (Submitted). google scholar
  • Dragomir, S., Ornea, L., 1998, Locally conformal Kahler geometry, Birkhauser: Boston, Basel, Berlin. google scholar
  • Falcitelli, M., Lanus, S., Pastore, A.M., 2004, Riemannian Submersion and Related Topics, World Scientific Publishing Co. Pte. Ltd.: Singapore Gray, A., 1967, Pseudo-Riemannian Almost Product Manifolds and Submersions, Journal of Mathematics and Mechanics, (16)7, 715-737. google scholar
  • Gündüzalp, Y., 2020, Clairaut anti-invariant submersions from locally product Riemannian manifolds, Beitr. Algebra Geom., 61, 605-614. google scholar
  • Lee, J., Park, J.H., Şahin, B., Song, D.Y., 2015, Einstein conditions for the base space of anti-invariant Riemannian submersions and Clairaut submersions, Taiwanese J. Math., 19(4), 1145-1160. google scholar
  • Marrero, J.C., Rocha, J., 1994, Locally conformal Kaehler submersions, Geom. Dedicata, 52(3), 271-289. google scholar
  • O’Neill, B., 1966, The fundamental equations of a submersion, Mich. Math. J., 13, 458-469, google scholar
  • O’Neill, B. 1967 Submersions and Geodesics, Duke Math. J., 34(2), 363-373. google scholar
  • Şahin, B., 2017, Riemannian submersions, Riemannian maps in Hermitian geometry, and their application, Elsiever. google scholar
  • Taştan, H.M., Gerdan S., 2016, Clairaut anti-invariant submersions from Sasakian and Kenmotsu manifolds, Mediterr. J. Math., 14(6), 234-251. google scholar
  • Taştan, H.M., Gerdan Aydın, S., 2019, Clairaut anti-invariant submersions from cosymplectic manifolds, Honam Math. J., 41(4), 707-724. google scholar
  • Vaisman, I., 1980, Some curvature properties of locally conformal Kaehler manifolds, Trans. Amer. Math. Soc., 259, 439-447. google scholar
  • Watson, B., 1976, Almost Hermitian submersions, J. Differ. Geom., 11(1), 147-165. google scholar

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APA

Pirinççi, B., Çimen, Ç., & Ulusoy, D. (2023). Clairaut and Einstein conditions for locally conformal Kaehler submersions. Istanbul Journal of Mathematics, 1(1), 28-39. https://doi.org/10.26650/ijmath.2023.00003


AMA

Pirinççi B, Çimen Ç, Ulusoy D. Clairaut and Einstein conditions for locally conformal Kaehler submersions. Istanbul Journal of Mathematics. 2023;1(1):28-39. https://doi.org/10.26650/ijmath.2023.00003


ABNT

Pirinççi, B.; Çimen, Ç.; Ulusoy, D. Clairaut and Einstein conditions for locally conformal Kaehler submersions. Istanbul Journal of Mathematics, [Publisher Location], v. 1, n. 1, p. 28-39, 2023.


Chicago: Author-Date Style

Pirinççi, Beran, and Çağrıhan Çimen and Deniz Ulusoy. 2023. “Clairaut and Einstein conditions for locally conformal Kaehler submersions.” Istanbul Journal of Mathematics 1, no. 1: 28-39. https://doi.org/10.26650/ijmath.2023.00003


Chicago: Humanities Style

Pirinççi, Beran, and Çağrıhan Çimen and Deniz Ulusoy. “Clairaut and Einstein conditions for locally conformal Kaehler submersions.” Istanbul Journal of Mathematics 1, no. 1 (Sep. 2023): 28-39. https://doi.org/10.26650/ijmath.2023.00003


Harvard: Australian Style

Pirinççi, B & Çimen, Ç & Ulusoy, D 2023, 'Clairaut and Einstein conditions for locally conformal Kaehler submersions', Istanbul Journal of Mathematics, vol. 1, no. 1, pp. 28-39, viewed 21 Sep. 2023, https://doi.org/10.26650/ijmath.2023.00003


Harvard: Author-Date Style

Pirinççi, B. and Çimen, Ç. and Ulusoy, D. (2023) ‘Clairaut and Einstein conditions for locally conformal Kaehler submersions’, Istanbul Journal of Mathematics, 1(1), pp. 28-39. https://doi.org/10.26650/ijmath.2023.00003 (21 Sep. 2023).


MLA

Pirinççi, Beran, and Çağrıhan Çimen and Deniz Ulusoy. “Clairaut and Einstein conditions for locally conformal Kaehler submersions.” Istanbul Journal of Mathematics, vol. 1, no. 1, 2023, pp. 28-39. [Database Container], https://doi.org/10.26650/ijmath.2023.00003


Vancouver

Pirinççi B, Çimen Ç, Ulusoy D. Clairaut and Einstein conditions for locally conformal Kaehler submersions. Istanbul Journal of Mathematics [Internet]. 21 Sep. 2023 [cited 21 Sep. 2023];1(1):28-39. Available from: https://doi.org/10.26650/ijmath.2023.00003 doi: 10.26650/ijmath.2023.00003


ISNAD

Pirinççi, Beran - Çimen, Çağrıhan - Ulusoy, Deniz. “Clairaut and Einstein conditions for locally conformal Kaehler submersions”. Istanbul Journal of Mathematics 1/1 (Sep. 2023): 28-39. https://doi.org/10.26650/ijmath.2023.00003



TIMELINE


Submitted01.05.2023
Accepted01.06.2023
Published Online06.06.2023

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