Abstract
In this paper, we derive curvature identities for Lagrangian submersions from globally conformal Kaehler manifolds onto Rieman nian manifolds. Then, we give a relation between the horizontal lift of the curvature tensor of the base manifold and the curvature tensor of a fiber. We examine the necessary and sufficient conditions for the total manifolds of Lagrangian submersions to be Einstein. We also obtain Ricci, scalar, sectional, holomorphic bisectional and holomorphic sectional curvatures for these submer sions. Finally, we give some inequalities involving the scalar and Ricci curvatures, and we also provide Chen-Ricci inequality for Lagrangian submersions from globally conformal Kaehler space forms.
Keywords
Riemannian submersion Lagrangian submersion globally conformal Kaehler manifold Chen-Ricci inequality
References
- Chen, B.-Y., 1993, Some pinching and classification theorems for minimal submanifolds, Arch. Math. (Basel), 60(6), 568–578. google scholar
- Chen, B.-Y., 1999, Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimensions, Glasg. Math. J. 41(1), 33–41. google scholar
- Chen, B.-Y., 2005, A general optimal inequality for arbitrary Riemannian submanifolds, J. Inequal. Pure Appl. Math. 6(3), Article 77. google scholar
- D. Chinea, 1985, Almost contact metric submersions, Rendiconti del Circlo Mat. di Palermo Serie II, 34, 89-104. google scholar
- Çimen Ç., Pirinççi B., Taştan H.M., Ulusoy D., 2024, On locally conformal Kaehler submersions, I. Elec. J. Geo., 17(2), 507-518. google scholar
- Dragomir, S., Ornea, L., 1998, Locally conformal Kähler 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 google scholar
- Gray, A., 1967, Pseudo-Riemannian Almost Product Manifolds and Submersions, Journal of Mathematics and Mechanics, (16)7, 715-737. google scholar
- Gülbahar, M., Eken Meriç, Ş., Kılıç, E., 2017, Sharp inequalities involving the Ricci curvature for Riemannian submersions. Kragujev. J. Math., 41(2), 279–293. 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
- Pirinççi, B., Çimen, Ç., Ulusoy, D., 2023, Clairaut and Einstein conditions for locally conformal Kaehler submersions, Istanbul J. Math., 1(1), 28-39. google scholar
- Pirinççi, B., 2025, Lagrangian submersions with locally conformal Kähler structures, Mediterr. J. Math., 22, 5. google scholar
- Şahin, B., 2010, Anti-invariant Riemannian submersions from almost Hermitian manifolds, Central Eur. J. Math., 8(3), 437–447. google scholar
- Şahin, B., 2017, Riemannian submersions, Riemannian maps in Hermitian geometry, and their application, Elsiever. google scholar
- Taştan, H.M., 2014, On Lagrangian submersions, Hacettepe J. Math. Stat. 43(6), 993–1000. 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., 2017, Lagrangian submersions from normal almost contact manifolds, Filomat 31(12), 3885–3895. 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
- Vaisman, I., 1980, On locally and globally K”ahler manifolds, Trans. Amer. Math. Soc., 262(2), 533-542. google scholar
- Watson, B., 1976, Almost Hermitian submersions, J. Differ. Geom., 11(1), 147–165. google scholar
Details
| Primary Language | English |
|---|---|
| Subjects | Pure Mathematics (Other) |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | June 24, 2025 |
| Submission Date | April 20, 2025 |
| Acceptance Date | June 2, 2025 |
| Published in Issue | Year 2025 Volume: 3 Issue: 1 |
