Serhan EKER

Sabit Uzunluklu Harmonik 1−Form Kullanılarak ????? Dirac Operatörünün Özdeğerlerine Tahminler

Bu makalede, sıfır olmayan sabit uzunluklu harmonik 1-formu kabul eden (?≥3)−boyutlu kompakt bir Riemann ?????−manifoldu üzerinde tanımlı ????? Dirac operatörünün öz değeri için alt sınır elde ettik. Daha sonra, limit durumunda harmonik 1−formun paralel olduğunu gösterdik.

Anahtar Kelimeler:

Spin ve 〖Spin〗^c geometry, Dirac operatörü, Öz değer tahminleri

Eigenvalue Estimates Using Harmonic 1−Form of Constant Length for The ????? Dirac Operator

In this paper, we obtain a lower bound for the eigenvalue of the ????? Dirac operator on an (?≥3)−dimensional compact Riemannian Spin ?−manifold admitting a non−zero harmonic 1−form of constant length. Then we show that, in the limiting case, this 1−form is parallel.

Keywords:

Spin and 〖Spin〗^c geometry, Dirac operator, Estimation of eigenvalues,

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Bär C, 1992. Lower eigenvalue estimates for Dirac operators. Math. Ann., 239: 39-46.
Friedrich T, 1980. Der este Eigenwert des Dirac-Operators einer kompakten, Riemannschen Manningfaltigkeit nichtnegativer Skalarkrümmung. Math. Nach. 97: 117-146.
Friedrich T, 2000. Dirac operators in Riemannian geometry. Graduate Studies in Mathematics, American Mathematical Society, 25.
Habib G, 2007. Energy-Momentum tensor on foliations. J. Geom. Phys. 57: 2234-2248.
Herzlich M, Moroianu A, 1999. Generalized Killing spinors and conformal eigenvalue estimates for Spin^c manifold. Ann. Global Anal. Geom., 17: 341-370.
Hijazi O, 1986. A conformal lower bound fort he smallest eigenvalue of the Dirac operator and Killing spinors. Commun. Math. Phys. 104: 151-162.
Hijazi O, 1991. Premire valeur propre de l’ operateur de Dirac et nombre de Yamabe. Comptes rendus de l’ Academie des sciences, Serie 1, Mathematique, 313(12): 865-868.
Hijazi O, 1995. Lower bounds for the eigenvalues of the Dirac operator. J. Geom. Phys., 16: 27-38.
Lawson H.B, 1989. Spin Geometry. Princeton University Press., Princeton.
Lichnerowicz A, 1963. Spineurs harmoniques. C.R. Acad. Sci. Paris Ser. AB, 257.
Lichnerowicz A, 1988. Killing spinors according to O. Hijazi and Applications. Spinors in Physics and Geometry (Trieste 1986), World Scientific Publishing Singapore 1-19.
Lichnerowicz A, 1987. Spin manifolds. Killing spinors and the universality of the Hijazi inequality. Lett. Math. Phys., 3: 331-344.
Moroianu A, Ornea L, 2004. Eigenvalue estimates for the Dirac operator and harmonic 1-forms of constant length. C.R. Math. Acad. Sci. Paris, 338(7): 561-564.
Nakad R, 2010. Lower bounds for the eigenvalues of the Dirac operator on manifolds. J. Geom. Phys. 60(10): 1634-1642.
Salamon D, 1995. Spin geometry and Seiberg-Witten invariants. Zurich: ETH.