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Journals / Fundamentals of Contemporary Mathematical Sciences / 2022 / Cilt: 3 Sayı: 1

Conformal Hemi-Slant Riemannian Maps

Şener YANAN
Pages
57–74
Publication Date
2022-01-30
DOI
—
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AI Summary & Key Takeaways

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

Lastly, we introduce some geometric properties under the notion of pluri-harmonic map.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we define conformal hemi-slant Riemannian maps from an almost Hermitian manifold to a Riemannian manifold as a generalization of conformal anti-invariant Riemannian maps, conformal semi-invariant Riemannian maps and conformal slant Riemannian maps.
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Key Findings & Data:Then, we obtain integrability conditions for certain distributions which are included in the notion of hemi-slant Riemannian maps and investigate their leaves.
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Conclusion & Impact:Lastly, we introduce some geometric properties under the notion of pluri-harmonic map.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:submersion · Riemannian submersion · Riemannian map

Abstract

In this study, we define conformal hemi-slant Riemannian maps from an almost Hermitian manifold to a Riemannian manifold as a generalization of conformal anti-invariant Riemannian maps, conformal semi-invariant Riemannian maps and conformal slant Riemannian maps. Then, we obtain integrability conditions for certain distributions which are included in the notion of hemi-slant Riemannian maps and investigate their leaves. Also, we get totally geodesic conditions for this type maps. Lastly, we introduce some geometric properties under the notion of pluri-harmonic map.

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Cite This Article

YANAN, Ş. (2022). Conformal Hemi-Slant Riemannian Maps. Fundamentals of Contemporary Mathematical Sciences, Cilt: 3 Sayı: 1, 57–74. https://ajindex.com/articles/905761

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References (20)

  1. Akyol M.A., Şahin B., Conformal anti-invariant submersions from almost Hermitian manifolds, Turkish Journal of Mathematics, 40(1), 43-70, 2016.
  2. Akyol M.A., Şahin B., Conformal semi-invariant submersions, Communications in Contemporary Mathematics, 19(2), 1650011, 2017.
  3. Akyol M.A., Şahin B., Conformal slant submersions, Hacettepe Journal of Mathematics and Statistics, 48(1), 28-44, 2019.
  4. Baird P., Wood J.C., Harmonic Morphisms between Riemannian Manifolds, Clarendon Press, 2003.
  5. Chen B.Y., Riemannian Submanifolds: Handbook of Differential Geometry, Vol. I, 187-418, 2000.
  6. Falcitelli M., Ianus S., Pastore A.M., Riemannian Submersions and Related Topics, World Scientific, 2004.
  7. Fischer A.E., Riemannian maps between Riemannian manifolds, Contemporary Mathematics, 132, 331-366, 1992.
  8. Garcia-Rio E., Kupeli D.N., Semi-Riemannian Maps and Their Applications, Kluwer Academic, 1999.
  9. Kumar S., Kumar S., Pandey S., Prasad R., Conformal hemi-slant submersions from almost Hermitian manifolds, Communications of the Korean Mathematical Society, 35(3), 999-1018, 2020.
  10. Nore T., Second fundamental form of a map, Annali di Matematica Pura ed Applicata, 146, 281-310, 1986.
  11. Ohnita Y., On pluriharmonicity of stable harmonic maps, Journal of the London Mathematical Society, 2(35), 563-587, 1987. O’Neill B., The fundamental equations of a submersion, Michigan Mathematical Journal, 13(4), 458-469, 1966.
  12. Şahin B., Semi-invariant Riemannian maps from almost Hermitian manifolds, Indagationes Mathematicae, 23, 80-94, 2012.
  13. Şahin B., Slant Riemannian maps from almost Hermitian manifolds, Quaestiones Mathematicae, 36(3), 449-461, 2013.
  14. Şahin B., Hemi-slant Riemannian maps, Mediterranean Journal of Mathematics, 14(10), 2017.
  15. Şahin B., Riemannian Submersions, Riemannian Maps in Hermitian Geometry and Their Applications, Elsevier, 2017.
  16. Şahin B., Conformal Riemannian maps between Riemannian manifolds, their harmonicity and decomposition theorems, Acta Applicandae Mathematicae, 109(3), 829-847, 2010.
  17. Şahin B., Yanan Ş., Conformal Riemannian maps from almost Hermitian manifolds, Turkish Journal of Mathematics, 42(5), 2436-2451, 2018.
  18. Şahin B., Yanan Ş., Conformal semi-invariant Riemannian maps from almost Hermitian manifolds, Filomat, 33(4), 1125-1134, 2019.
  19. Yanan Ş., Conformal generic Riemannian maps from almost Hermitian manifolds, Turkish Journal of Science, 6(2), 76-88, 2021.
  20. Yanan Ş., Şahin B., Conformal slant Riemannian maps, International Journal of Maps in Mathematics, 2022 (Accepted).