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Journals / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 5

Almost h-conformal semi-invariant submersions from almost quaternionic Hermitian manifolds

Kwang Soon PARK
Pages
1804–1824
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, we give some examples of such maps.

📌 3 Key Takeaways

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Objective & Hypothesis:As a generalization of Riemannian submersions, horizontally conformal submersions, semi-invariant submersions, h-semi-invariant submersions, almost h-semi-invariant submersions, conformal semi-invariant submersions, we introduce h-conformal semi-invariant submersions and almost h-conformal semi-invariant submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds.
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Key Findings & Data:We study their properties: the geometry of foliations, the conditions for total manifolds to be locally product manifolds, the conditions for such maps to be totally geodesic.
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Conclusion & Impact:Finally, we give some examples of such maps.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:horizontally conformal submersion · quaternionic manifold · totally geodesic

Abstract

As a generalization of Riemannian submersions, horizontally conformal submersions, semi-invariant submersions, h-semi-invariant submersions, almost h-semi-invariant submersions, conformal semi-invariant submersions, we introduce h-conformal semi-invariant submersions and almost h-conformal semi-invariant submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds. We study their properties: the geometry of foliations, the conditions for total manifolds to be locally product manifolds, the conditions for such maps to be totally geodesic. Finally, we give some examples of such maps.

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Cite This Article

PARK, K. S. (2022). Almost h-conformal semi-invariant submersions from almost quaternionic Hermitian manifolds. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 5, 1804–1824. https://ajindex.com/articles/529560

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References (19)

  1. M.A. Akyol and B. Sahin, Conformal anti-invariant submersions from almost Her- mitian manifolds, Turkish J. Math. 40 (1), 43–70, 2016
  2. M.A. Akyol and B. Sahin, Conformal semi-invariant submersions, Commun. Con- temp. Math. 19 (2), 1650011, 2017
  3. D.V. Alekseevsky and S. Marchiafava, Almost complex submanifolds of quaternionic manifolds, In: Proceedings of the colloquium on differential geometry, Debrecen (Hun- gary), 25-30 July 2000, Inst. Math. Inform. Debrecen, 23-38, 2001
  4. P. Baird and J.C. Wood, Harmonic morphisms between Riemannian manifolds, Ox- ford Science Publications, 2003
  5. M. Barros, B.Y. Chen and F. Urbano, Quaternion CR-submanifolds of quaternion manifolds, Kodai Math. J. 4, 399–417, 1980
  6. A.L. Besse, Einstein manifolds, Springer Verlag, Berlin, 1987
  7. J.P. Bourguignon and H.B. Lawson, Stability and isolation phenomena for Yang-mills fields, Commum. Math. Phys. 79, 189–230, 1981
  8. J.P. Bourguignon and H.B. Lawson, A mathematician’s visit to Kaluza-Klein theory, Rend. Semin. Mat. Torino Fasc. Spec. 1989, 143–163, 1989
  9. B.Y. Chen, Geometry of slant submanifolds, Katholieke Universiteit Leuven, Leuven, 1990
  10. V. Cortés, C. Mayer, T. Mohaupt and F. Saueressig, Special geometry of Euclidean supersymmetry 1. Vector multiplets, J. High Energy Phys. 3, 028, 2004
  11. A. Gray, Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech. 16, 715–737, 1967
  12. S. Gudmundsson, The geometry of harmonic morphisms, Ph.D. thesis, University of Leeds, 1992
  13. M. Falcitelli, S. Ianus and A.M. Pastore, Riemannian submersions and related topics, World Scientific Publishing Co., 2004
  14. B. Fuglede, Harmonic morphisms between Riemannian manifolds, Ann. Inst. Fourier (Grenoble), 28 (2), 107–144, 1978
  15. S. Ianus, R. Mazzocco and G.E. Vilcu, Riemannian submersions from quaternionic manifolds, Acta. Appl. Math. 104, 83–89, 2008
  16. S. Ianus and M. Visinescu, Kaluza-Klein theory with scalar fields and generalized Hopf manifolds, Class. Quantum Gravity, 4, 1317–1325, 1987
  17. S. Ianus and M. Visinescu, Space-time compactification and Riemannian submersions, In: Rassias, G.(ed.) The Mathematical Heritage of C. F. Gauss, 358-371, World Scientific, River Edge, 1991
  18. T. Ishihara, A mapping of Riemannian manifolds which preserves harmonic functions, J. Math. Kyoto University, 19 (2), 215–229, 1979
  19. M.T. Mustafa, Applications of harmonic morphisms to gravity, J. Math. Phys. 41 (10), 6918–6929, 2000.