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Year 2022, Volume: 71 Issue: 4, 1007 - 1022, 30.12.2022

Mehmet Gülbahar Şemsi Eken Meriç Erol Kılıç

https://doi.org/10.31801/cfsuasmas.990670
Cited By: 1

Abstract

References

  • Alegre, P., Chen, B. Y., Munteanu, M. I., Riemannian submersions, δ-invariants and optimal inequality, Ann. Glob. Anal. Geom., 42 (2010), 317–331. https://doi.org/10.1007/s10455-012-9314-4
  • Altafini, C., Redundant robotic chains on Riemannian submersions, IEEE Robot. Autom., 20(2) (2004), 335–340. https://doi.org/10.1109/TRA.2004.824636
  • Arslan, K., Ezenta¸s, R., Mihai, I, Murathan C., Özgür, C., B.Y Chen inequalities for submanifolds in locally conformal almost cosymplectic manifolds, Bull. Inst. Math. Acad. Sin., 29(3) (2001), 231–242.
  • Aytimur, H., Özgür, C., Sharp inequalities for anti-invariant Riemannian submersions from Sasakian space forms, J. Geom. Phys., 166 (2021), 104251. https://doi.org/10.1016/j.geomphys.2021.104251
  • Besse, A. L., Einstein Manifolds, Berlin-Heidelberg-New York, Spinger-Verlag, 1987.
  • Bhattacharyaa, R., Patrangenarub, V., Nonparametic estimation of location and dispersion on Riemannian manifolds, J. Statist. Plann. Inference, 108 (2002), 23–35. https://doi.org/10.1016/S0378-3758(02)00268-9
  • Chen, B. Y., Some pinching and classification theorems for minimal submanifolds, Arch. Math., 60 (1993), 568–578. https://doi.org/10.1007/BF01236084
  • Chen, B. Y., A Riemannian invariant and its applications to submanifold theory, Results Math., 27 (1995), 17–28. https://doi.org/10.1007/BF03322265
  • Chen, B. Y., Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimensions, Glasgow Math. J., 41 (1999), 33–41. https://doi.org/10.1017/S0017089599970271
  • Chen, B. Y., Pseudo-Riemannian Geometry, δ-Invariants and Applications, World Scientific Publishing, Hackensack, NJ, 2011.
  • Chen, B. Y., Dillen, F., Verstraelen, L., δ-invariants and their applications to centroaffine geometry, Differ. Geom. Appl., 22, (2005) 341–354. https://doi.org/10.1016/j.difgeo.2005.01.008
  • Eken Meri¸c, S., Gülbahar, M., Kılı¸c, E., Some inequalities for Riemannian submersions, An. Stiint. Univ. Al. I. Cuza Iasi. Mat., 63 (2017), 471-482.
  • Falcitelli, M., Ianus, S., Pastore, A. M., Visinescu, M., Some applications of Riemannian submersions in physics, Rev. Roum. Phys., 48 (2003), 627–639.
  • Falcitelli, M., Ianus, S., Pastore, A. M., Riemannian Submersions and Related Topics, World Scientific Company, 2004.
  • Gülbahar, M., Eken Meri¸c, S., Kılı¸c, E., Sharp inequalities involving the Ricci curvature for Riemannian submersions, Kragujevac J. Math., 42(2) (2017). https://doi.org/10.5937/KgJMath1702279G
  • Kennedy, L. C., Some Results on Einstein Metrics on Two Classes of Quotient Manifolds, PhD thesis, University of California, 2003.
  • Kobayashi, S., Submersions of CR-submanifolds, Tohoku Math. J., 89 (1987), 95–100. https://doi.org/10.2748/tmj/1178228372
  • Memoli F., Sapiro G., Thompson P., Implicit brain imaging, Neuro Image, 23 (2004), 179–188. https://doi.org/10.1016/j.neuroimage.2004.07.072
  • Poyraz, N., Ya¸sar, E., Chen-like inequalities on lightlike hypersurface of a Lorentzian product manifold with quarter-symmetric nonmetric connection, Kragujevac J. Math., 40 (2016), 146–164. https://doi.org/10.5937/kgjmath1602146p
  • Şahin, B., Riemannian submersions from almost Hermitian manifolds, Taiwan. J. Math., 17 (2013), 629–659. https://doi.org/10.11650/tjm.17.2013.2191
  • Şahin, B., Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and Their Applications, Academic Press, 2017.
  • Siddiqui, A. N., Chen inequalities for statistical submersions between statistical manifolds, Int. J. Geom. Methods Mod. Phys., 18 (2021), 2150049. https://doi.org/10.1142/S0219887821500493
  • Uddin, S., Solamy, F. R., Shahid, M. H., Saloom, A., B.-Y. Chen’s inequality for biwarped products and its applications in Kenmotsu manifolds, Mediterr. J. Math., 15 (2018). https://doi.org/10.1007/s00009-018-1238-1
  • Vilcu, G. E., On Chen invariants and inequalities in quaternionic geometry, J. Inequal. Appl., 2013:66 (2013). https://doi.org/10.1186/1029-242X-2013-66
  • Wang, H., Ziller, W., Einstein metrics on principal torus bundles, J. Differ. Geo., 31 (1990), 215–248.
  • Zhao, H., Kelly, A. R., Zhou, J., Lu, J., Yang, Y. Y., Graph attribute embedding via Riemannian submersion learning. Comput. Vis. Image Underst., 115 (2011), 962–975. https://doi.org/10.1016/j.cviu.2010.12.005

Chen invariants for Riemannian submersions and their applications

Year 2022, Volume: 71 Issue: 4, 1007 - 1022, 30.12.2022

Mehmet Gülbahar Şemsi Eken Meriç Erol Kılıç

https://doi.org/10.31801/cfsuasmas.990670
Cited By: 1

Abstract

In this paper, an optimal inequality involving the delta curvature is exposed. With the help of this inequality some characterizations about the vertical motion and the horizontal divergence are obtained.

Keywords

Curvature Riemannian submersion horizontal divergence

References

  • Alegre, P., Chen, B. Y., Munteanu, M. I., Riemannian submersions, δ-invariants and optimal inequality, Ann. Glob. Anal. Geom., 42 (2010), 317–331. https://doi.org/10.1007/s10455-012-9314-4
  • Altafini, C., Redundant robotic chains on Riemannian submersions, IEEE Robot. Autom., 20(2) (2004), 335–340. https://doi.org/10.1109/TRA.2004.824636
  • Arslan, K., Ezenta¸s, R., Mihai, I, Murathan C., Özgür, C., B.Y Chen inequalities for submanifolds in locally conformal almost cosymplectic manifolds, Bull. Inst. Math. Acad. Sin., 29(3) (2001), 231–242.
  • Aytimur, H., Özgür, C., Sharp inequalities for anti-invariant Riemannian submersions from Sasakian space forms, J. Geom. Phys., 166 (2021), 104251. https://doi.org/10.1016/j.geomphys.2021.104251
  • Besse, A. L., Einstein Manifolds, Berlin-Heidelberg-New York, Spinger-Verlag, 1987.
  • Bhattacharyaa, R., Patrangenarub, V., Nonparametic estimation of location and dispersion on Riemannian manifolds, J. Statist. Plann. Inference, 108 (2002), 23–35. https://doi.org/10.1016/S0378-3758(02)00268-9
  • Chen, B. Y., Some pinching and classification theorems for minimal submanifolds, Arch. Math., 60 (1993), 568–578. https://doi.org/10.1007/BF01236084
  • Chen, B. Y., A Riemannian invariant and its applications to submanifold theory, Results Math., 27 (1995), 17–28. https://doi.org/10.1007/BF03322265
  • Chen, B. Y., Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimensions, Glasgow Math. J., 41 (1999), 33–41. https://doi.org/10.1017/S0017089599970271
  • Chen, B. Y., Pseudo-Riemannian Geometry, δ-Invariants and Applications, World Scientific Publishing, Hackensack, NJ, 2011.
  • Chen, B. Y., Dillen, F., Verstraelen, L., δ-invariants and their applications to centroaffine geometry, Differ. Geom. Appl., 22, (2005) 341–354. https://doi.org/10.1016/j.difgeo.2005.01.008
  • Eken Meri¸c, S., Gülbahar, M., Kılı¸c, E., Some inequalities for Riemannian submersions, An. Stiint. Univ. Al. I. Cuza Iasi. Mat., 63 (2017), 471-482.
  • Falcitelli, M., Ianus, S., Pastore, A. M., Visinescu, M., Some applications of Riemannian submersions in physics, Rev. Roum. Phys., 48 (2003), 627–639.
  • Falcitelli, M., Ianus, S., Pastore, A. M., Riemannian Submersions and Related Topics, World Scientific Company, 2004.
  • Gülbahar, M., Eken Meri¸c, S., Kılı¸c, E., Sharp inequalities involving the Ricci curvature for Riemannian submersions, Kragujevac J. Math., 42(2) (2017). https://doi.org/10.5937/KgJMath1702279G
  • Kennedy, L. C., Some Results on Einstein Metrics on Two Classes of Quotient Manifolds, PhD thesis, University of California, 2003.
  • Kobayashi, S., Submersions of CR-submanifolds, Tohoku Math. J., 89 (1987), 95–100. https://doi.org/10.2748/tmj/1178228372
  • Memoli F., Sapiro G., Thompson P., Implicit brain imaging, Neuro Image, 23 (2004), 179–188. https://doi.org/10.1016/j.neuroimage.2004.07.072
  • Poyraz, N., Ya¸sar, E., Chen-like inequalities on lightlike hypersurface of a Lorentzian product manifold with quarter-symmetric nonmetric connection, Kragujevac J. Math., 40 (2016), 146–164. https://doi.org/10.5937/kgjmath1602146p
  • Şahin, B., Riemannian submersions from almost Hermitian manifolds, Taiwan. J. Math., 17 (2013), 629–659. https://doi.org/10.11650/tjm.17.2013.2191
  • Şahin, B., Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and Their Applications, Academic Press, 2017.
  • Siddiqui, A. N., Chen inequalities for statistical submersions between statistical manifolds, Int. J. Geom. Methods Mod. Phys., 18 (2021), 2150049. https://doi.org/10.1142/S0219887821500493
  • Uddin, S., Solamy, F. R., Shahid, M. H., Saloom, A., B.-Y. Chen’s inequality for biwarped products and its applications in Kenmotsu manifolds, Mediterr. J. Math., 15 (2018). https://doi.org/10.1007/s00009-018-1238-1
  • Vilcu, G. E., On Chen invariants and inequalities in quaternionic geometry, J. Inequal. Appl., 2013:66 (2013). https://doi.org/10.1186/1029-242X-2013-66
  • Wang, H., Ziller, W., Einstein metrics on principal torus bundles, J. Differ. Geo., 31 (1990), 215–248.
  • Zhao, H., Kelly, A. R., Zhou, J., Lu, J., Yang, Y. Y., Graph attribute embedding via Riemannian submersion learning. Comput. Vis. Image Underst., 115 (2011), 962–975. https://doi.org/10.1016/j.cviu.2010.12.005
There are 26 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Research Articles
Authors

Mehmet Gülbahar 0000-0001-6950-7633

Şemsi Eken Meriç This is me 0000-0003-2783-1149

Erol Kılıç 0000-0001-7536-0404

Publication Date December 30, 2022
Submission Date September 6, 2021
Acceptance Date May 25, 2022
Published in Issue Year 2022 Volume: 71 Issue: 4

Cite

APA Gülbahar, M., Eken Meriç, Ş., & Kılıç, E. (2022). Chen invariants for Riemannian submersions and their applications. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 71(4), 1007-1022. https://doi.org/10.31801/cfsuasmas.990670
AMA Gülbahar M, Eken Meriç Ş, Kılıç E. Chen invariants for Riemannian submersions and their applications. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. December 2022;71(4):1007-1022. doi:10.31801/cfsuasmas.990670
Chicago Gülbahar, Mehmet, Şemsi Eken Meriç, and Erol Kılıç. “Chen Invariants for Riemannian Submersions and Their Applications”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71, no. 4 (December 2022): 1007-22. https://doi.org/10.31801/cfsuasmas.990670.
EndNote Gülbahar M, Eken Meriç Ş, Kılıç E (December 1, 2022) Chen invariants for Riemannian submersions and their applications. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71 4 1007–1022.
IEEE M. Gülbahar, Ş. Eken Meriç, and E. Kılıç, “Chen invariants for Riemannian submersions and their applications”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 71, no. 4, pp. 1007–1022, 2022, doi: 10.31801/cfsuasmas.990670.
ISNAD Gülbahar, Mehmet et al. “Chen Invariants for Riemannian Submersions and Their Applications”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71/4 (December 2022), 1007-1022. https://doi.org/10.31801/cfsuasmas.990670.
JAMA Gülbahar M, Eken Meriç Ş, Kılıç E. Chen invariants for Riemannian submersions and their applications. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71:1007–1022.
MLA Gülbahar, Mehmet et al. “Chen Invariants for Riemannian Submersions and Their Applications”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 71, no. 4, 2022, pp. 1007-22, doi:10.31801/cfsuasmas.990670.
Vancouver Gülbahar M, Eken Meriç Ş, Kılıç E. Chen invariants for Riemannian submersions and their applications. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71(4):1007-22.

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