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On the almost h-conformal semi-slant Riemannian maps

Year 2024, Volume: 53 Issue: 5, 1333 - 1353, 15.10.2024
https://doi.org/10.15672/hujms.1113123

Abstract

As a generalization of conformal semi-slant submersions, semi-slant Riemannian maps, almost h-semi-slant submersions and almost h-semi-slant Riemannian maps, we introduce almost h-conformal semi-slant submersions and almost h-conformal semi-slant Riemannian maps. We give some examples of such maps and also introduce some types of pluriharmonic maps, invariant maps and geodesic maps. We study the geometry of foliations, the integrability of distributions, the properties of pluriharmonic maps, invariant maps and geodesic maps. We also investigate the condition for such maps to be totally geodesic and the harmonicity of such maps.

References

  • [1] M. A. Akyol, Conformal semi-slant submersions, International Journal of Geometric Methods in Modern Physics, 14(07), 1750114, 2017.
  • [2] M. A. Akyol and B. Sahin, Conformal anti-invariant submersions from almost Hermitian manifolds, Turkish Journal of Mathematics, 40(1), 43-70, 2016.
  • [3] M. A. Akyol and B. Sahin, Conformal semi-invariant submersions, Communications in Contemporary Mathematics, 19(2), 1650011, 2017.
  • [4] P. Baird and J. C. Wood, Harmonic morphisms between Riemannian manifolds, Oxford science publications, 2003.
  • [5] J. P. Bourguignon and H. B. Lawson, Stability and isolation phenomena for Yangmills fields, Commum. Math. Phys. 79, 189-230, 1981.
  • [6] V. Cortés, C. Mayer, T. Mohaupt and F. Saueressig, Special geometry of Euclidean supersymmetry 1. Vector multiplets, J. High Energy Phys. 2004(03), 028, 2004.
  • [7] M. Falcitelli, S. Ianus and A. M. Pastore, Riemannian submersions and related topics, World Scientific Publishing Co. 2004.
  • [8] A. E. Fischer, Riemannian maps between Riemannian manifolds, Contemporary Math. 132, 331-366, 1992.
  • [9] B. Fuglede, Harmonic morphisms between Riemannian manifolds, Ann. Inst. Fourier (Grenoble), 28, 107-144, 1978.
  • [10] A. Gray, Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech, 16, 715-737, 1967.
  • [11] S. Ianus, R. Mazzocco and G. E. Vilcu, Riemannian submersions from quaternionic manifolds, Acta. Appl. Math. 104, 83-89, 2008.
  • [12] S. Ianus and M. Visinescu, Kaluza-Klein theory with scalar fields and generalized Hopf manifolds, Class. Quantum Gravity, 4, 1317-1325, 1987.
  • [13] T. Ishihara, A mapping of Riemannian manifolds which preserves harmonic functions, Journal of Mathematics of Kyoto University, 19(2), 215-229, 1979.
  • [14] M. Jin, Y. Wang, S. T. Yau and X. Gu, Optimal global conformal surface parameterization, IEEE Visualization 2004, 267-274, 2004.
  • [15] M. T. Mustafa, Applications of harmonic morphisms to gravity, J. Math. Phys. 41(10), 6918-6929, 2000.
  • [16] Y. Ohnita, On Pluriharmonicity of Stable Harmonic Maps, Journal of the London Mathematical Society, s2-35(3), 563-568, 1987.
  • [17] B. O’Neill, The fundamental equations of a submersion, Mich. Math. J. 13, 458-469, 1966.
  • [18] K. S. Park, Almost h-semi-slant Riemannian maps, Taiwanese Journal of Mathematics, 17(3), 937-956, 2013.
  • [19] K. S. Park, H-semi-slant submersions from almost quaternionic Hermitian manifolds, Taiwanese Journal of Mathematics, 18(6), 1909-1926, 2014.
  • [20] K. S. Park, Semi-slant Riemannian map, Quaestiones Mathematicae, 41(1), 1-14, 2018.
  • [21] K. S. Park, Almost h-conformal semi-invariant submersions from almost quaternionic Hermitian manifolds, Hacettepe Journal of Mathematics and Statistics, 49(5), 1804 - 1824, 2020.
  • [22] B. Sahin, Conformal Riemannian maps between Riemannian manifolds, their harmonicity and decomposition theorems, Acta applicandae mathematicae, 109(3), 829-847, 2010.
  • [23] B. Sahin and S. Yanan, Conformal semi-invariant Riemannian maps from almost Hermitian manifolds, Filomat, 33(4), 1125-1134, 2019.
  • [24] H. Urakawa, Calculus of variations and harmonic maps, American Mathematical Soc. 2013.
  • [25] Y. Wang, X. Gu and S. T. Yau, Volumetric harmonic map, Communications in Information and Systems, 3(3), 191-202, 2003.
  • [26] Y. Wang, J. Shi, X. Yin, X. Gu, T. F. Chan, S. T. Yau, A. W. Toga and P. M. Thompson, Brain surface conformal parameterization with the Ricci flow, IEEE transactions on medical imaging, 31(2), 251-264, 2011.
Year 2024, Volume: 53 Issue: 5, 1333 - 1353, 15.10.2024
https://doi.org/10.15672/hujms.1113123

Abstract

References

  • [1] M. A. Akyol, Conformal semi-slant submersions, International Journal of Geometric Methods in Modern Physics, 14(07), 1750114, 2017.
  • [2] M. A. Akyol and B. Sahin, Conformal anti-invariant submersions from almost Hermitian manifolds, Turkish Journal of Mathematics, 40(1), 43-70, 2016.
  • [3] M. A. Akyol and B. Sahin, Conformal semi-invariant submersions, Communications in Contemporary Mathematics, 19(2), 1650011, 2017.
  • [4] P. Baird and J. C. Wood, Harmonic morphisms between Riemannian manifolds, Oxford science publications, 2003.
  • [5] J. P. Bourguignon and H. B. Lawson, Stability and isolation phenomena for Yangmills fields, Commum. Math. Phys. 79, 189-230, 1981.
  • [6] V. Cortés, C. Mayer, T. Mohaupt and F. Saueressig, Special geometry of Euclidean supersymmetry 1. Vector multiplets, J. High Energy Phys. 2004(03), 028, 2004.
  • [7] M. Falcitelli, S. Ianus and A. M. Pastore, Riemannian submersions and related topics, World Scientific Publishing Co. 2004.
  • [8] A. E. Fischer, Riemannian maps between Riemannian manifolds, Contemporary Math. 132, 331-366, 1992.
  • [9] B. Fuglede, Harmonic morphisms between Riemannian manifolds, Ann. Inst. Fourier (Grenoble), 28, 107-144, 1978.
  • [10] A. Gray, Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech, 16, 715-737, 1967.
  • [11] S. Ianus, R. Mazzocco and G. E. Vilcu, Riemannian submersions from quaternionic manifolds, Acta. Appl. Math. 104, 83-89, 2008.
  • [12] S. Ianus and M. Visinescu, Kaluza-Klein theory with scalar fields and generalized Hopf manifolds, Class. Quantum Gravity, 4, 1317-1325, 1987.
  • [13] T. Ishihara, A mapping of Riemannian manifolds which preserves harmonic functions, Journal of Mathematics of Kyoto University, 19(2), 215-229, 1979.
  • [14] M. Jin, Y. Wang, S. T. Yau and X. Gu, Optimal global conformal surface parameterization, IEEE Visualization 2004, 267-274, 2004.
  • [15] M. T. Mustafa, Applications of harmonic morphisms to gravity, J. Math. Phys. 41(10), 6918-6929, 2000.
  • [16] Y. Ohnita, On Pluriharmonicity of Stable Harmonic Maps, Journal of the London Mathematical Society, s2-35(3), 563-568, 1987.
  • [17] B. O’Neill, The fundamental equations of a submersion, Mich. Math. J. 13, 458-469, 1966.
  • [18] K. S. Park, Almost h-semi-slant Riemannian maps, Taiwanese Journal of Mathematics, 17(3), 937-956, 2013.
  • [19] K. S. Park, H-semi-slant submersions from almost quaternionic Hermitian manifolds, Taiwanese Journal of Mathematics, 18(6), 1909-1926, 2014.
  • [20] K. S. Park, Semi-slant Riemannian map, Quaestiones Mathematicae, 41(1), 1-14, 2018.
  • [21] K. S. Park, Almost h-conformal semi-invariant submersions from almost quaternionic Hermitian manifolds, Hacettepe Journal of Mathematics and Statistics, 49(5), 1804 - 1824, 2020.
  • [22] B. Sahin, Conformal Riemannian maps between Riemannian manifolds, their harmonicity and decomposition theorems, Acta applicandae mathematicae, 109(3), 829-847, 2010.
  • [23] B. Sahin and S. Yanan, Conformal semi-invariant Riemannian maps from almost Hermitian manifolds, Filomat, 33(4), 1125-1134, 2019.
  • [24] H. Urakawa, Calculus of variations and harmonic maps, American Mathematical Soc. 2013.
  • [25] Y. Wang, X. Gu and S. T. Yau, Volumetric harmonic map, Communications in Information and Systems, 3(3), 191-202, 2003.
  • [26] Y. Wang, J. Shi, X. Yin, X. Gu, T. F. Chan, S. T. Yau, A. W. Toga and P. M. Thompson, Brain surface conformal parameterization with the Ricci flow, IEEE transactions on medical imaging, 31(2), 251-264, 2011.
There are 26 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Kwang-soon Park 0000-0002-6539-6216

Early Pub Date April 14, 2024
Publication Date October 15, 2024
Published in Issue Year 2024 Volume: 53 Issue: 5

Cite

APA Park, K.-s. (2024). On the almost h-conformal semi-slant Riemannian maps. Hacettepe Journal of Mathematics and Statistics, 53(5), 1333-1353. https://doi.org/10.15672/hujms.1113123
AMA Park Ks. On the almost h-conformal semi-slant Riemannian maps. Hacettepe Journal of Mathematics and Statistics. October 2024;53(5):1333-1353. doi:10.15672/hujms.1113123
Chicago Park, Kwang-soon. “On the Almost H-Conformal Semi-Slant Riemannian Maps”. Hacettepe Journal of Mathematics and Statistics 53, no. 5 (October 2024): 1333-53. https://doi.org/10.15672/hujms.1113123.
EndNote Park K-s (October 1, 2024) On the almost h-conformal semi-slant Riemannian maps. Hacettepe Journal of Mathematics and Statistics 53 5 1333–1353.
IEEE K.-s. Park, “On the almost h-conformal semi-slant Riemannian maps”, Hacettepe Journal of Mathematics and Statistics, vol. 53, no. 5, pp. 1333–1353, 2024, doi: 10.15672/hujms.1113123.
ISNAD Park, Kwang-soon. “On the Almost H-Conformal Semi-Slant Riemannian Maps”. Hacettepe Journal of Mathematics and Statistics 53/5 (October 2024), 1333-1353. https://doi.org/10.15672/hujms.1113123.
JAMA Park K-s. On the almost h-conformal semi-slant Riemannian maps. Hacettepe Journal of Mathematics and Statistics. 2024;53:1333–1353.
MLA Park, Kwang-soon. “On the Almost H-Conformal Semi-Slant Riemannian Maps”. Hacettepe Journal of Mathematics and Statistics, vol. 53, no. 5, 2024, pp. 1333-5, doi:10.15672/hujms.1113123.
Vancouver Park K-s. On the almost h-conformal semi-slant Riemannian maps. Hacettepe Journal of Mathematics and Statistics. 2024;53(5):1333-5.