Research Article
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Semi-slant lightlike submersions

Year 2024, Volume: 73 Issue: 4, 982 - 996
https://doi.org/10.31801/cfsuasmas.1430102

Abstract

In this paper, we intend to study semi-slant lightlike submersions from indefinite Kaehler manifolds onto lightlike manifolds. After giving definitions and basic properties, we obtain conditions for a lightlike submersion to be a semi-slant lightlike submersion. We indicate some relevant examples. Finally, we investigate the geometric properties of foliations that appeared with a semi-slant lightlike submersion.

References

  • Akyol, M. A., Gündüzalp, Y., Semi-invariant semi Riemannian submersions, Commun. Fac. Sci. Univ. Ank. Series A1, 67(1) (2018), 80-92. https://doi.org/10.1501/Commua1-000000832
  • Altafini, C., Redundant robotic chains on Riemannian submersions, IEEE ,Transactions on Robotics and Automation, 20(2) (2004), 335-340. https://doi.org/10.1109/TRA.2004.824636
  • Bourguignon, J. P., Lawson, H. B., Stability and isolation phenomena for Yang-mills fields, Commun. Math. Phys., 79 (1981), 189-230.
  • Bourguignon, J. P., Lawson, H. B., A mathematician’s visit to Kaluza-Klein theory, Rend. Sem. Mat. Univ. Politec. Torino, Special Issue, (1989), 143-163.
  • Duggal, K. L., Harmonic maps, morphisms and globally null manifolds, Int. J. of Pure and App. Math., 6(4) (2003), 421-438.
  • Falcitelli, M., Ianus, S., Pastore, A. M., Riemannian Submersions and Related Topics, World Scientific, River Edge, NJ, 2004.
  • Gray, A., Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech., 16 (1967), 715-737.
  • Gündüzalp, Y., Anti-invariant semi-Riemannian submersions from almost para-Hermitian manifolds, Journal of Function Spaces and Applications, (2013), Article ID 720623.
  • Gündüzalp, Y., Slant submersions from almost product Riemannian manifolds, Turkish J. Math., 37 (2013), 863-873. https://doi.org/10.3906/mat-1205-64
  • Gündüzalp, Y., Semi-slant submersions from almost product Riemannian manifolds, Demonstratio Mathematica, 49(3) (2016), 345-356. https://doi.org/10.1515/dema-2016-0029
  • Ianus, S., Visinescu, M., Kaluza-Klein theory with scalar fields and generalized Hopf manifolds, Class. Quantum Gravity, 4 (1987), 1317-1325.
  • Kaushal, R., Kumar, R., Kumar Nagaich, R., On geometry of pointwise slant lightlike submersions with totally umbilical fibers, Afrika Mathematica, 33(1) (2022), 22. https://doi.org/10.1007/s13370-022-00963-4
  • Ianus, S., Visinescu, M., Space-time compaction and Riemannian submersions, The Mathematical Heritage of C. F. Gauss,River Edge, World Scientific, (1991), 358-371.
  • Mustafa, M. T., Applications of harmonic morphisms to gravity, J. Math. Phys., 41 (2000), 6918-6929. https://doi.org/10.1063/1.1290381
  • O’Neill, B., The fundamental equations of a submersion, Mich. Math. J., 13 (1966), 458-469.
  • O’Neill, B., Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York-London, 1983.
  • Park, K. S., Prasad, R., Semi-slant submersions, Bull. Korean Math. Soc., 50(3) (2013), 951-962. https://doi.org/10.4134/BKMS.2012.49.2.329
  • Prasad, R., Kumar Singh, P., Kumar, S., Slant lightlike submersions from an indefinite nearly Kaehler manidolds into a lightlike manifold, J. Math. Comput. Sci., 8 (2018), 324-349. https://doi.org/10.28919/jmcs/3561
  • Sachdeva, R., Kumar, R., Bhatia, S. S., Slant lightlike submersions from an indefinite almost Hermitian manifold into a lightlike manifold, Ukrainian Mathematical Journal, 68(7) (2016), 225-240. https://doi.org/10.1007/s11253-016-1280-8
  • Shukla, S. S., Omar, S., Yadav, S. K., Screen slant lightlike submersions, J. Appl. Math. Informatic, 40(5-6) (2022), 1073-1082. https://doi.org/10.1134/S1995080222060300
  • Şahin, B., Screen conformal submersions between lightlike manifolds and semi-Riemannian manifolds and their harmonicity, International Journal of Geometric Methods in Modern Physics, 4(6) (2007), 987-1003. https://doi.org/10.1142/S0219887807002405
  • Şahin, B., On a submersion between Reinhart lightlike manifolds and semi-Riemannian manifolds, Mediterr. J. Math., 5 (2008), 273-284. https://doi.org/10.1007/s00009-008-0149-y
  • Şahin, B., Slant submersions from almost Hermitian manifolds, Bull. Math. Soc. Sci. Math. Roumanie, 1 (2011), 93-105.
  • Şahin, B., Riemannian Submersions, Riemannian Maps in Hermitian Geometry and Their Applications, Elsevier, Academic Press, 2017.
  • Şahin, B., Gündüzalp, Y., Submersions from semi-Riemannian manifolds onto lightlike manifolds, Hacet. J. Math. Stat., 39 (2010), 41-53.
  • Vilcu, G. E., New class of semi-Riemannian submersions, Romanian Journal of Physics, 54(9-10) (2009), 815-821.
  • Watson, B., G, G’-Riemannian submersions and nonlinear gauge field equations of general relativity, Teubner-Texte Math., (1983), 324-349.
Year 2024, Volume: 73 Issue: 4, 982 - 996
https://doi.org/10.31801/cfsuasmas.1430102

Abstract

References

  • Akyol, M. A., Gündüzalp, Y., Semi-invariant semi Riemannian submersions, Commun. Fac. Sci. Univ. Ank. Series A1, 67(1) (2018), 80-92. https://doi.org/10.1501/Commua1-000000832
  • Altafini, C., Redundant robotic chains on Riemannian submersions, IEEE ,Transactions on Robotics and Automation, 20(2) (2004), 335-340. https://doi.org/10.1109/TRA.2004.824636
  • Bourguignon, J. P., Lawson, H. B., Stability and isolation phenomena for Yang-mills fields, Commun. Math. Phys., 79 (1981), 189-230.
  • Bourguignon, J. P., Lawson, H. B., A mathematician’s visit to Kaluza-Klein theory, Rend. Sem. Mat. Univ. Politec. Torino, Special Issue, (1989), 143-163.
  • Duggal, K. L., Harmonic maps, morphisms and globally null manifolds, Int. J. of Pure and App. Math., 6(4) (2003), 421-438.
  • Falcitelli, M., Ianus, S., Pastore, A. M., Riemannian Submersions and Related Topics, World Scientific, River Edge, NJ, 2004.
  • Gray, A., Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech., 16 (1967), 715-737.
  • Gündüzalp, Y., Anti-invariant semi-Riemannian submersions from almost para-Hermitian manifolds, Journal of Function Spaces and Applications, (2013), Article ID 720623.
  • Gündüzalp, Y., Slant submersions from almost product Riemannian manifolds, Turkish J. Math., 37 (2013), 863-873. https://doi.org/10.3906/mat-1205-64
  • Gündüzalp, Y., Semi-slant submersions from almost product Riemannian manifolds, Demonstratio Mathematica, 49(3) (2016), 345-356. https://doi.org/10.1515/dema-2016-0029
  • Ianus, S., Visinescu, M., Kaluza-Klein theory with scalar fields and generalized Hopf manifolds, Class. Quantum Gravity, 4 (1987), 1317-1325.
  • Kaushal, R., Kumar, R., Kumar Nagaich, R., On geometry of pointwise slant lightlike submersions with totally umbilical fibers, Afrika Mathematica, 33(1) (2022), 22. https://doi.org/10.1007/s13370-022-00963-4
  • Ianus, S., Visinescu, M., Space-time compaction and Riemannian submersions, The Mathematical Heritage of C. F. Gauss,River Edge, World Scientific, (1991), 358-371.
  • Mustafa, M. T., Applications of harmonic morphisms to gravity, J. Math. Phys., 41 (2000), 6918-6929. https://doi.org/10.1063/1.1290381
  • O’Neill, B., The fundamental equations of a submersion, Mich. Math. J., 13 (1966), 458-469.
  • O’Neill, B., Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York-London, 1983.
  • Park, K. S., Prasad, R., Semi-slant submersions, Bull. Korean Math. Soc., 50(3) (2013), 951-962. https://doi.org/10.4134/BKMS.2012.49.2.329
  • Prasad, R., Kumar Singh, P., Kumar, S., Slant lightlike submersions from an indefinite nearly Kaehler manidolds into a lightlike manifold, J. Math. Comput. Sci., 8 (2018), 324-349. https://doi.org/10.28919/jmcs/3561
  • Sachdeva, R., Kumar, R., Bhatia, S. S., Slant lightlike submersions from an indefinite almost Hermitian manifold into a lightlike manifold, Ukrainian Mathematical Journal, 68(7) (2016), 225-240. https://doi.org/10.1007/s11253-016-1280-8
  • Shukla, S. S., Omar, S., Yadav, S. K., Screen slant lightlike submersions, J. Appl. Math. Informatic, 40(5-6) (2022), 1073-1082. https://doi.org/10.1134/S1995080222060300
  • Şahin, B., Screen conformal submersions between lightlike manifolds and semi-Riemannian manifolds and their harmonicity, International Journal of Geometric Methods in Modern Physics, 4(6) (2007), 987-1003. https://doi.org/10.1142/S0219887807002405
  • Şahin, B., On a submersion between Reinhart lightlike manifolds and semi-Riemannian manifolds, Mediterr. J. Math., 5 (2008), 273-284. https://doi.org/10.1007/s00009-008-0149-y
  • Şahin, B., Slant submersions from almost Hermitian manifolds, Bull. Math. Soc. Sci. Math. Roumanie, 1 (2011), 93-105.
  • Şahin, B., Riemannian Submersions, Riemannian Maps in Hermitian Geometry and Their Applications, Elsevier, Academic Press, 2017.
  • Şahin, B., Gündüzalp, Y., Submersions from semi-Riemannian manifolds onto lightlike manifolds, Hacet. J. Math. Stat., 39 (2010), 41-53.
  • Vilcu, G. E., New class of semi-Riemannian submersions, Romanian Journal of Physics, 54(9-10) (2009), 815-821.
  • Watson, B., G, G’-Riemannian submersions and nonlinear gauge field equations of general relativity, Teubner-Texte Math., (1983), 324-349.
There are 27 citations in total.

Details

Primary Language English
Subjects Algebraic and Differential Geometry
Journal Section Research Articles
Authors

Ramazan Sarı 0000-0002-4618-8243

Publication Date
Submission Date February 1, 2024
Acceptance Date September 2, 2024
Published in Issue Year 2024 Volume: 73 Issue: 4

Cite

APA Sarı, R. (n.d.). Semi-slant lightlike submersions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 73(4), 982-996. https://doi.org/10.31801/cfsuasmas.1430102
AMA Sarı R. Semi-slant lightlike submersions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 73(4):982-996. doi:10.31801/cfsuasmas.1430102
Chicago Sarı, Ramazan. “Semi-Slant Lightlike Submersions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73, no. 4 n.d.: 982-96. https://doi.org/10.31801/cfsuasmas.1430102.
EndNote Sarı R Semi-slant lightlike submersions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73 4 982–996.
IEEE R. Sarı, “Semi-slant lightlike submersions”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 73, no. 4, pp. 982–996, doi: 10.31801/cfsuasmas.1430102.
ISNAD Sarı, Ramazan. “Semi-Slant Lightlike Submersions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73/4 (n.d.), 982-996. https://doi.org/10.31801/cfsuasmas.1430102.
JAMA Sarı R. Semi-slant lightlike submersions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.;73:982–996.
MLA Sarı, Ramazan. “Semi-Slant Lightlike Submersions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 73, no. 4, pp. 982-96, doi:10.31801/cfsuasmas.1430102.
Vancouver Sarı R. Semi-slant lightlike submersions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 73(4):982-96.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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