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Year 2022, , 1621 - 1629, 01.12.2022
https://doi.org/10.15672/hujms.1054157

Abstract

References

  • [1] C. Bär, Extrinsic Bounds for Eigenvalues of the Dirac Operator, Ann. Glob. Anal. Geom. 16 (6), 573–596, 1998.
  • [2] S. Eker, Seiberg−Witten-like equations on the strictly pseudoconvex CR−3 manifolds, Miskolc Math. Notes, 20 (1), 233–43, 2019.
  • [3] S. Eker, Lower Bound Eigenvalue Problems of the Compact Riemannian Spin- Submanifold Dirac Operator, Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, (special issue I), 13, 56–62, 2020.
  • [4] S. Eker, Lower Bounds for the Eigenvalues of the Dirac Operator on Spinc Manifolds, Iran. J. Sci. Technol. Trans. A Sci., 44, 251–257, 2020.
  • [5] T. Friedrich, Dirac operators in Riemannian geometry, Graduate Studies in Mathematics, 25, Amer. Math. Soc., Providence, RI, 2000.
  • [6] T. Friedrich and E.C. Kim, Some remarks on the Hijazi inequality and generalizations of the Killing equation for spinors, J. Geom. Phys. 37 (1-2), 1–14, 2001.
  • [7] N. Ginoux and B. Morel, On eigenvalue estimates for the submanifold Dirac operator, Internat. J. Math. 13 (5), 553–548, 2002.
  • [8] G. Habib, Energy-Momentum tensor on foliations, J. Geom. Phys. 57, 2234–2248, 2007.
  • [9] M. Herzlich and A. Moroianu, Generalized Killing spinors and conformal eigenvalue estimates for Spinc manifolds, Ann. Global Anal. Geom. 17, 341–370, 1999.
  • [10] O. Hijazi, A conformal lower bound for the smallest eigenvalue of the Dirac operator and Killing spinors, Comm. Math. Phys. 104, 151–162, 1986.
  • [11] O. Hijazi, Lower bounds for the eigenvalues of the Dirac operator, J. Geom. Phys, 16, 27–38, 1995.
  • [12] O. Hijazi and X. Zhang, Lower bounds for the eigenvalues of the Dirac operator: part I. The hypersurface Dirac operator, Ann. Global Anal. Geom. 19 (4), 355–376, 2001.
  • [13] O. Hijazi and X. Zhang, Lower Bounds for the Eigenvalues of the Dirac Operator: Part II. The Submanifold Dirac Operator, Ann. Global Anal. Geom. 20 (2), 163–181, 2001.
  • [14] O. Hijazi, S. Montiel and X. Zhang, Eigenvalues of the Dirac Operator on Manifolds with Boundary, Comm. Math. Phys. 221 (2), 255–265, 2001.
  • [15] H. Lawson and M. Michelsohn, Spin geometry, Princeton university press, 1989.
  • [16] A. Lichnerowicz, Spineurs harmoniques, C.R. Acad. Sci. Paris Ser. AB, 257, 1963.
  • [17] R. Nakad, Lower bounds for the eigenvalues of the Dirac operator on Spinc manifolds, J. Geom. Phys. 60 (10), 1634–1642, 2010.
  • [18] R. Nakad and J. Roth, Lower bounds for the eigenvalues of the Spinc Dirac operator on submanifolds, Arch. Math. 104 (5), 453–461, 2015.
  • [19] D. Salamon, Spin geometry adn Seiberg−Witten invariants, Citeseer, 1996.
  • [20] E. Witten, Monopoles and four-manifolds, Math. Ress. Lett. 1 (6), 769–796, 1994.
  • [21] X.Zhang, Lower bounds for eigenvalues of hypersurface Dirac operators, Math. Res. Lett. 5 (2), 199–210, 1998.

Estimation on the Spin${}^c$ twisted Dirac operators

Year 2022, , 1621 - 1629, 01.12.2022
https://doi.org/10.15672/hujms.1054157

Abstract

We generalize the lower bound estimates for eigenvalues of the twisted Dirac operator on compact Riemannian Spincc−submanifold obtained by Roger Nakad and Julien Roth in (Archiv der Mathematik 104(5), 453-461, 2015).

References

  • [1] C. Bär, Extrinsic Bounds for Eigenvalues of the Dirac Operator, Ann. Glob. Anal. Geom. 16 (6), 573–596, 1998.
  • [2] S. Eker, Seiberg−Witten-like equations on the strictly pseudoconvex CR−3 manifolds, Miskolc Math. Notes, 20 (1), 233–43, 2019.
  • [3] S. Eker, Lower Bound Eigenvalue Problems of the Compact Riemannian Spin- Submanifold Dirac Operator, Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, (special issue I), 13, 56–62, 2020.
  • [4] S. Eker, Lower Bounds for the Eigenvalues of the Dirac Operator on Spinc Manifolds, Iran. J. Sci. Technol. Trans. A Sci., 44, 251–257, 2020.
  • [5] T. Friedrich, Dirac operators in Riemannian geometry, Graduate Studies in Mathematics, 25, Amer. Math. Soc., Providence, RI, 2000.
  • [6] T. Friedrich and E.C. Kim, Some remarks on the Hijazi inequality and generalizations of the Killing equation for spinors, J. Geom. Phys. 37 (1-2), 1–14, 2001.
  • [7] N. Ginoux and B. Morel, On eigenvalue estimates for the submanifold Dirac operator, Internat. J. Math. 13 (5), 553–548, 2002.
  • [8] G. Habib, Energy-Momentum tensor on foliations, J. Geom. Phys. 57, 2234–2248, 2007.
  • [9] M. Herzlich and A. Moroianu, Generalized Killing spinors and conformal eigenvalue estimates for Spinc manifolds, Ann. Global Anal. Geom. 17, 341–370, 1999.
  • [10] O. Hijazi, A conformal lower bound for the smallest eigenvalue of the Dirac operator and Killing spinors, Comm. Math. Phys. 104, 151–162, 1986.
  • [11] O. Hijazi, Lower bounds for the eigenvalues of the Dirac operator, J. Geom. Phys, 16, 27–38, 1995.
  • [12] O. Hijazi and X. Zhang, Lower bounds for the eigenvalues of the Dirac operator: part I. The hypersurface Dirac operator, Ann. Global Anal. Geom. 19 (4), 355–376, 2001.
  • [13] O. Hijazi and X. Zhang, Lower Bounds for the Eigenvalues of the Dirac Operator: Part II. The Submanifold Dirac Operator, Ann. Global Anal. Geom. 20 (2), 163–181, 2001.
  • [14] O. Hijazi, S. Montiel and X. Zhang, Eigenvalues of the Dirac Operator on Manifolds with Boundary, Comm. Math. Phys. 221 (2), 255–265, 2001.
  • [15] H. Lawson and M. Michelsohn, Spin geometry, Princeton university press, 1989.
  • [16] A. Lichnerowicz, Spineurs harmoniques, C.R. Acad. Sci. Paris Ser. AB, 257, 1963.
  • [17] R. Nakad, Lower bounds for the eigenvalues of the Dirac operator on Spinc manifolds, J. Geom. Phys. 60 (10), 1634–1642, 2010.
  • [18] R. Nakad and J. Roth, Lower bounds for the eigenvalues of the Spinc Dirac operator on submanifolds, Arch. Math. 104 (5), 453–461, 2015.
  • [19] D. Salamon, Spin geometry adn Seiberg−Witten invariants, Citeseer, 1996.
  • [20] E. Witten, Monopoles and four-manifolds, Math. Ress. Lett. 1 (6), 769–796, 1994.
  • [21] X.Zhang, Lower bounds for eigenvalues of hypersurface Dirac operators, Math. Res. Lett. 5 (2), 199–210, 1998.
There are 21 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Serhan Eker 0000-0003-1039-0551

Publication Date December 1, 2022
Published in Issue Year 2022

Cite

APA Eker, S. (2022). Estimation on the Spin${}^c$ twisted Dirac operators. Hacettepe Journal of Mathematics and Statistics, 51(6), 1621-1629. https://doi.org/10.15672/hujms.1054157
AMA Eker S. Estimation on the Spin${}^c$ twisted Dirac operators. Hacettepe Journal of Mathematics and Statistics. December 2022;51(6):1621-1629. doi:10.15672/hujms.1054157
Chicago Eker, Serhan. “Estimation on the Spin${}^c$ Twisted Dirac Operators”. Hacettepe Journal of Mathematics and Statistics 51, no. 6 (December 2022): 1621-29. https://doi.org/10.15672/hujms.1054157.
EndNote Eker S (December 1, 2022) Estimation on the Spin${}^c$ twisted Dirac operators. Hacettepe Journal of Mathematics and Statistics 51 6 1621–1629.
IEEE S. Eker, “Estimation on the Spin${}^c$ twisted Dirac operators”, Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 6, pp. 1621–1629, 2022, doi: 10.15672/hujms.1054157.
ISNAD Eker, Serhan. “Estimation on the Spin${}^c$ Twisted Dirac Operators”. Hacettepe Journal of Mathematics and Statistics 51/6 (December 2022), 1621-1629. https://doi.org/10.15672/hujms.1054157.
JAMA Eker S. Estimation on the Spin${}^c$ twisted Dirac operators. Hacettepe Journal of Mathematics and Statistics. 2022;51:1621–1629.
MLA Eker, Serhan. “Estimation on the Spin${}^c$ Twisted Dirac Operators”. Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 6, 2022, pp. 1621-9, doi:10.15672/hujms.1054157.
Vancouver Eker S. Estimation on the Spin${}^c$ twisted Dirac operators. Hacettepe Journal of Mathematics and Statistics. 2022;51(6):1621-9.