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Some Estimates for the Spin−Submanifold Twisted Dirac Operators

Yıl 2020, Cilt: 5 Sayı: 1, 8 - 15, 30.03.2020

Öz

In this paper, we generalize lower bound estimates for the eigenvalue estimates of the submanifold twisted Dirac operator on a compact Riemannian Spin−submanifold proved by N. Ginoux and B. Morel in 2002.

Kaynakça

  • Bar, C. (1998). Extrinsic Bounds for Eigenvalues of the Dirac Operator. Ann. Glob. Anal. Geom., 16(6), 573–596.
  • Eker, S., Degirmenci, N. (2018). Seiberg −Witten−like equations without Self−Duality on odd dimensional manifolds. Journal of Partial Differential Equations, 31(4), 291–303.
  • Eker, S. (2019). The Bochner vanishing theorems on the conformal killing vector fields, TWMS Journal of Applied and Engineering Mathematics, 9(1) Special Issue, 114–120.
  • Eker, S . (2020). Lower Bound Eigenvalue Problems of the Compact Riemannian Spin-Submanifold Dirac Operator. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 13 (OZEL SAYI I) , 56–62.
  • Eker, S. (2020). Lower Bounds for the Eigenvalues of the Dirac Operator on Spinc Manifolds. Iranian Journal of Science and Technology, Transactions A: Science, 44(1), 251—257.
  • Friedrich, T. (1980). Der erste Eigenwert des Dirac-Operators einer kompakten, Riemannschen Mannigfaltigkeit nichtnegativer Skalarkrümmung. Mathematische Nachrichten, 97(1), 117–146.
  • Friedrich, T. (2001). Some remarks on the Hijazi inequality and generalizations of the Killing equation for spinors. Journal of Geometry and Physics, 37(1-2), 1–14.
  • Ginoux, N., Bertrand, M. (2002). On eigenvalue estimates for the submanifold Dirac operator. International Journal of Mathematics, 13(05), 533-548.
  • Hijazi, O. (1986). A conformal lower bound for the smallest eigenvalue of the Dirac operator and Killing spinors. Communications in Mathematical Physics, 104(1), 151–162.
  • Hijazi, O. (1991). Premiere valeur propre de l'opérateur de Dirac et nombre de Yamabe. Comptes rendus de l’Académie des sciences. Série 1, Mathématique, 313(12), 865–868.
  • Hijazi, O. (1995). Lower bounds for the eigenvalues of the Dirac operator. Journal of Geometry and Physics, 16(1), 27–38.
  • Hijazi, O., Xiao, Z. (2001). Lower Bounds for the Eigenvalues of the Dirac Operator: Part II. The Submanifold Dirac Operator. Annals of Global Analysis and Geometry, 20(2), 163–181.
  • Hijazi, O., Xiao, Z. (2001). Lower Bounds for the Eigenvalues of the Dirac Operator: Part II. The Submanifold Dirac Operator. Annals of Global Analysis and Geometry, 20(2), 163–181.
  • Hijazi, O., Montiel, S., Xiao, Z. (2001). Eigenvalues of the Dirac Operator on Manifolds with Boundary. Communications in Mathematical Physics, 221(2), 255–265.
  • Lawson, H.B., Michelsohn, M.L. (2016). Spin geometry. Princeton university press, 38.
  • Lichnerowicz, O. (1963). Spineurs harmoniques. C.R. Acad. Sci. Paris Ser. A–B, 257.
  • Morel, B. (2001). Eigenvalue estimates for the Dirac–Schrödinger operators. Journal of Geometry and Physics, 38(1), 1–18.
  • Adriana, T. (2009). On the twisted Dirac operators. Bull. Math. Soc. Sci. Math. Roumanie Tome, 52(3), 383–386.
  • Xiao, Z. (1998). Lower bounds for eigenvalues of hypersurface Dirac operators. Mathematical Research Letters, 5(2), 199–210.
  • Witten, E. (1981). A new proof of the positive energy theorem. Communications in Mathematical Physics, 80(3), 381–402.
Yıl 2020, Cilt: 5 Sayı: 1, 8 - 15, 30.03.2020

Öz

Kaynakça

  • Bar, C. (1998). Extrinsic Bounds for Eigenvalues of the Dirac Operator. Ann. Glob. Anal. Geom., 16(6), 573–596.
  • Eker, S., Degirmenci, N. (2018). Seiberg −Witten−like equations without Self−Duality on odd dimensional manifolds. Journal of Partial Differential Equations, 31(4), 291–303.
  • Eker, S. (2019). The Bochner vanishing theorems on the conformal killing vector fields, TWMS Journal of Applied and Engineering Mathematics, 9(1) Special Issue, 114–120.
  • Eker, S . (2020). Lower Bound Eigenvalue Problems of the Compact Riemannian Spin-Submanifold Dirac Operator. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 13 (OZEL SAYI I) , 56–62.
  • Eker, S. (2020). Lower Bounds for the Eigenvalues of the Dirac Operator on Spinc Manifolds. Iranian Journal of Science and Technology, Transactions A: Science, 44(1), 251—257.
  • Friedrich, T. (1980). Der erste Eigenwert des Dirac-Operators einer kompakten, Riemannschen Mannigfaltigkeit nichtnegativer Skalarkrümmung. Mathematische Nachrichten, 97(1), 117–146.
  • Friedrich, T. (2001). Some remarks on the Hijazi inequality and generalizations of the Killing equation for spinors. Journal of Geometry and Physics, 37(1-2), 1–14.
  • Ginoux, N., Bertrand, M. (2002). On eigenvalue estimates for the submanifold Dirac operator. International Journal of Mathematics, 13(05), 533-548.
  • Hijazi, O. (1986). A conformal lower bound for the smallest eigenvalue of the Dirac operator and Killing spinors. Communications in Mathematical Physics, 104(1), 151–162.
  • Hijazi, O. (1991). Premiere valeur propre de l'opérateur de Dirac et nombre de Yamabe. Comptes rendus de l’Académie des sciences. Série 1, Mathématique, 313(12), 865–868.
  • Hijazi, O. (1995). Lower bounds for the eigenvalues of the Dirac operator. Journal of Geometry and Physics, 16(1), 27–38.
  • Hijazi, O., Xiao, Z. (2001). Lower Bounds for the Eigenvalues of the Dirac Operator: Part II. The Submanifold Dirac Operator. Annals of Global Analysis and Geometry, 20(2), 163–181.
  • Hijazi, O., Xiao, Z. (2001). Lower Bounds for the Eigenvalues of the Dirac Operator: Part II. The Submanifold Dirac Operator. Annals of Global Analysis and Geometry, 20(2), 163–181.
  • Hijazi, O., Montiel, S., Xiao, Z. (2001). Eigenvalues of the Dirac Operator on Manifolds with Boundary. Communications in Mathematical Physics, 221(2), 255–265.
  • Lawson, H.B., Michelsohn, M.L. (2016). Spin geometry. Princeton university press, 38.
  • Lichnerowicz, O. (1963). Spineurs harmoniques. C.R. Acad. Sci. Paris Ser. A–B, 257.
  • Morel, B. (2001). Eigenvalue estimates for the Dirac–Schrödinger operators. Journal of Geometry and Physics, 38(1), 1–18.
  • Adriana, T. (2009). On the twisted Dirac operators. Bull. Math. Soc. Sci. Math. Roumanie Tome, 52(3), 383–386.
  • Xiao, Z. (1998). Lower bounds for eigenvalues of hypersurface Dirac operators. Mathematical Research Letters, 5(2), 199–210.
  • Witten, E. (1981). A new proof of the positive energy theorem. Communications in Mathematical Physics, 80(3), 381–402.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Volume V, Issue I, 2020
Yazarlar

Mehmet Ergen

Yayımlanma Tarihi 30 Mart 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 5 Sayı: 1

Kaynak Göster

APA Ergen, M. (2020). Some Estimates for the Spin−Submanifold Twisted Dirac Operators. Turkish Journal of Science, 5(1), 8-15.
AMA Ergen M. Some Estimates for the Spin−Submanifold Twisted Dirac Operators. TJOS. Mart 2020;5(1):8-15.
Chicago Ergen, Mehmet. “Some Estimates for the Spin−Submanifold Twisted Dirac Operators”. Turkish Journal of Science 5, sy. 1 (Mart 2020): 8-15.
EndNote Ergen M (01 Mart 2020) Some Estimates for the Spin−Submanifold Twisted Dirac Operators. Turkish Journal of Science 5 1 8–15.
IEEE M. Ergen, “Some Estimates for the Spin−Submanifold Twisted Dirac Operators”, TJOS, c. 5, sy. 1, ss. 8–15, 2020.
ISNAD Ergen, Mehmet. “Some Estimates for the Spin−Submanifold Twisted Dirac Operators”. Turkish Journal of Science 5/1 (Mart 2020), 8-15.
JAMA Ergen M. Some Estimates for the Spin−Submanifold Twisted Dirac Operators. TJOS. 2020;5:8–15.
MLA Ergen, Mehmet. “Some Estimates for the Spin−Submanifold Twisted Dirac Operators”. Turkish Journal of Science, c. 5, sy. 1, 2020, ss. 8-15.
Vancouver Ergen M. Some Estimates for the Spin−Submanifold Twisted Dirac Operators. TJOS. 2020;5(1):8-15.