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Dergiler / Konuralp Journal of Mathematics / 2026 / Volume: 5 Issue: 1

THE EQUIVALENCE OF TWO APPROACHES OF SEIBERG-WITTEN EQUATIONS IN 8-DIMENSION

SERHAN Eker(Ağrı İbrahim Çeçen University, Science and Art Faculty, Department of Mathematics, Ağrı, Turkey)
Sayfa
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Yayın Tarihi
2017-04-03
DOI
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Finally we show the equivalence between them.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Seiberg-Witten equations which are formed by Dirac equation and Curvature-equation, have some generalizations on 8􀀀dimensional manifold [1, 3, 5].
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Temel Bulgular & Veri:In this paper we consider the $Spin^c$-structure which was given in [1].
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Sonuç & Katkı:Finally we show the equivalence between them.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Seiberg-Witten equations · spinor · Dirac operator

Abstract

Seiberg-Witten equations which are formed by Dirac equation and Curvature-equation, have some generalizations on 8􀀀dimensional manifold [1, 3, 5]. In this paper we consider the $Spin^c$-structure which was given in [1]. Then by using this $Spin^c$-structure, we examine the curvature equations which were given in [1, 3]. Finally we show the equivalence between them.

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Bu Makaleye Atıf Yap

Eker, S. (2017). THE EQUIVALENCE OF TWO APPROACHES OF SEIBERG-WITTEN EQUATIONS IN 8-DIMENSION. Konuralp Journal of Mathematics, Volume: 5 Issue: 1. https://ajindex.com/articles/1521856

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Kaynakça (8)

  1. A.H. Bilge, T. Dereli and S. Kocak, Monopole equations on 8􀀀manifolds with Spin(7) holonomy, Commun. Math. Phys. Vol:203, No.1 (1999), 21-30.
  2. Salamon, D., Spin geometry and Seiberg-Witten invariants, Preprint.
  3. N. Degirmenci and N.  Ozdemir, Seiberg-Witten like equations on 8-manifold with Structure Group Spin(7), Journal of Dynamical Systems and Geometric Theories Vol:7, No:1 (2009), 21-39.
  4. Friedrich T., Dirac operators in Riemannian geometry, Graduate Studies in Mathematics, American Mathematical Society, Providence, Rhlode Island, 25; 2000.
  5. Gao YH., Tian G., Instantons and the monopole-like equations in eight dimensions, J High Energy Phys 2000; 5: 036.
  6. Witten, E., Monopoles and four manifolds, Math Res Lett 1994; 1: 769-796.
  7. Gao YH., Tian G., Instantons and the monopole-like equations in eight dimensions, J High Energy Phys 2000; 5: 036.
  8. Witten, E., Monopoles and four manifolds, Math Res Lett 1994; 1: 769-796.