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

Abstract

In this paper, we obtain a lower bound for the eigenvalue of the 𝑆𝑝𝑖𝑛𝑐 Dirac operator on an (𝑑≥3)−dimensional compact Riemannian Spin 𝑐−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

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

Abstract

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

Keywords

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

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