Research Article
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Year 2022, , 57 - 74, 30.01.2022
https://doi.org/10.54974/fcmathsci.1033708

Abstract

References

  • Akyol M.A., Şahin B., Conformal anti-invariant submersions from almost Hermitian manifolds, Turkish Journal of Mathematics, 40(1), 43-70, 2016.
  • Akyol M.A., Şahin B., Conformal semi-invariant submersions, Communications in Contemporary Mathematics, 19(2), 1650011, 2017.
  • Akyol M.A., Şahin B., Conformal slant submersions, Hacettepe Journal of Mathematics and Statistics, 48(1), 28-44, 2019.
  • Baird P., Wood J.C., Harmonic Morphisms between Riemannian Manifolds, Clarendon Press, 2003.
  • Chen B.Y., Riemannian Submanifolds: Handbook of Differential Geometry, Vol. I, 187-418, 2000.
  • Falcitelli M., Ianus S., Pastore A.M., Riemannian Submersions and Related Topics, World Scientific, 2004.
  • Fischer A.E., Riemannian maps between Riemannian manifolds, Contemporary Mathematics, 132, 331-366, 1992.
  • Garcia-Rio E., Kupeli D.N., Semi-Riemannian Maps and Their Applications, Kluwer Academic, 1999.
  • 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.
  • Nore T., Second fundamental form of a map, Annali di Matematica Pura ed Applicata, 146, 281-310, 1986.
  • 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.
  • Şahin B., Semi-invariant Riemannian maps from almost Hermitian manifolds, Indagationes Mathematicae, 23, 80-94, 2012.
  • Şahin B., Slant Riemannian maps from almost Hermitian manifolds, Quaestiones Mathematicae, 36(3), 449-461, 2013.
  • Şahin B., Hemi-slant Riemannian maps, Mediterranean Journal of Mathematics, 14(10), 2017.
  • Şahin B., Riemannian Submersions, Riemannian Maps in Hermitian Geometry and Their Applications, Elsevier, 2017.
  • Şahin B., Conformal Riemannian maps between Riemannian manifolds, their harmonicity and decomposition theorems, Acta Applicandae Mathematicae, 109(3), 829-847, 2010.
  • Şahin B., Yanan Ş., Conformal Riemannian maps from almost Hermitian manifolds, Turkish Journal of Mathematics, 42(5), 2436-2451, 2018.
  • Şahin B., Yanan Ş., Conformal semi-invariant Riemannian maps from almost Hermitian manifolds, Filomat, 33(4), 1125-1134, 2019.
  • Yanan Ş., Conformal generic Riemannian maps from almost Hermitian manifolds, Turkish Journal of Science, 6(2), 76-88, 2021.
  • Yanan Ş., Şahin B., Conformal slant Riemannian maps, International Journal of Maps in Mathematics, 2022 (Accepted).
  • Yano K., Kon M., Structures on Manifolds: Series in Pure Mathematics, World Scientific, 1984.

Conformal Hemi-Slant Riemannian Maps

Year 2022, , 57 - 74, 30.01.2022
https://doi.org/10.54974/fcmathsci.1033708

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.

References

  • Akyol M.A., Şahin B., Conformal anti-invariant submersions from almost Hermitian manifolds, Turkish Journal of Mathematics, 40(1), 43-70, 2016.
  • Akyol M.A., Şahin B., Conformal semi-invariant submersions, Communications in Contemporary Mathematics, 19(2), 1650011, 2017.
  • Akyol M.A., Şahin B., Conformal slant submersions, Hacettepe Journal of Mathematics and Statistics, 48(1), 28-44, 2019.
  • Baird P., Wood J.C., Harmonic Morphisms between Riemannian Manifolds, Clarendon Press, 2003.
  • Chen B.Y., Riemannian Submanifolds: Handbook of Differential Geometry, Vol. I, 187-418, 2000.
  • Falcitelli M., Ianus S., Pastore A.M., Riemannian Submersions and Related Topics, World Scientific, 2004.
  • Fischer A.E., Riemannian maps between Riemannian manifolds, Contemporary Mathematics, 132, 331-366, 1992.
  • Garcia-Rio E., Kupeli D.N., Semi-Riemannian Maps and Their Applications, Kluwer Academic, 1999.
  • 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.
  • Nore T., Second fundamental form of a map, Annali di Matematica Pura ed Applicata, 146, 281-310, 1986.
  • 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.
  • Şahin B., Semi-invariant Riemannian maps from almost Hermitian manifolds, Indagationes Mathematicae, 23, 80-94, 2012.
  • Şahin B., Slant Riemannian maps from almost Hermitian manifolds, Quaestiones Mathematicae, 36(3), 449-461, 2013.
  • Şahin B., Hemi-slant Riemannian maps, Mediterranean Journal of Mathematics, 14(10), 2017.
  • Şahin B., Riemannian Submersions, Riemannian Maps in Hermitian Geometry and Their Applications, Elsevier, 2017.
  • Şahin B., Conformal Riemannian maps between Riemannian manifolds, their harmonicity and decomposition theorems, Acta Applicandae Mathematicae, 109(3), 829-847, 2010.
  • Şahin B., Yanan Ş., Conformal Riemannian maps from almost Hermitian manifolds, Turkish Journal of Mathematics, 42(5), 2436-2451, 2018.
  • Şahin B., Yanan Ş., Conformal semi-invariant Riemannian maps from almost Hermitian manifolds, Filomat, 33(4), 1125-1134, 2019.
  • Yanan Ş., Conformal generic Riemannian maps from almost Hermitian manifolds, Turkish Journal of Science, 6(2), 76-88, 2021.
  • Yanan Ş., Şahin B., Conformal slant Riemannian maps, International Journal of Maps in Mathematics, 2022 (Accepted).
  • Yano K., Kon M., Structures on Manifolds: Series in Pure Mathematics, World Scientific, 1984.
There are 22 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Şener Yanan 0000-0003-1600-6522

Publication Date January 30, 2022
Published in Issue Year 2022

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19113 FCMS is licensed under the Creative Commons Attribution 4.0 International Public License.