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Yıl 2022, Cilt: 71 Sayı: 4, 1007 - 1022, 30.12.2022

Mehmet Gülbahar Şemsi Eken Meriç Erol Kılıç

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

Öz

Kaynakça

  • 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

Yıl 2022, Cilt: 71 Sayı: 4, 1007 - 1022, 30.12.2022

Mehmet Gülbahar Şemsi Eken Meriç Erol Kılıç

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

Öz

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.

Anahtar Kelimeler

Curvature Riemannian submersion horizontal divergence

Kaynakça

  • 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
Toplam 26 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Uygulamalı Matematik
Bölüm Research Article
Yazarlar

Mehmet Gülbahar 0000-0001-6950-7633

Şemsi Eken Meriç Bu kişi benim 0000-0003-2783-1149

Erol Kılıç 0000-0001-7536-0404

Yayımlanma Tarihi 30 Aralık 2022
Gönderilme Tarihi 6 Eylül 2021
Kabul Tarihi 25 Mayıs 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 71 Sayı: 4

Kaynak Göster

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. Aralık 2022;71(4):1007-1022. doi:10.31801/cfsuasmas.990670
Chicago Gülbahar, Mehmet, Şemsi Eken Meriç, ve Erol Kılıç. “Chen Invariants for Riemannian Submersions and Their Applications”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71, sy. 4 (Aralık 2022): 1007-22. https://doi.org/10.31801/cfsuasmas.990670.
EndNote Gülbahar M, Eken Meriç Ş, Kılıç E (01 Aralık 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, ve E. Kılıç, “Chen invariants for Riemannian submersions and their applications”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 71, sy. 4, ss. 1007–1022, 2022, doi: 10.31801/cfsuasmas.990670.
ISNAD Gülbahar, Mehmet vd. “Chen Invariants for Riemannian Submersions and Their Applications”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71/4 (Aralık 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 vd. “Chen Invariants for Riemannian Submersions and Their Applications”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 71, sy. 4, 2022, ss. 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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Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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