Lower Bound Eigenvalue Problems of the Compact Riemannian Spin-Submanifold Dirac Operator

Öz

In this paper, we construct two modified spinorial LeviCivita connection based on the EnergyMomentum tensor and its trace to bring an optimal lower bound to the eigenvalues of the compact Riemannian Spinsubmanifold Dirac operator in terms of the the EnergyMomentum tensor and its trace.  Then, we extend these estimates in terms of the Yamabe number and the area of the submanifold under the conformal change of the metric.

Anahtar Kelimeler

• Spin and 〖Spin〗^c geometry,Dirac operator

Kompakt Riemannian Spin-Alt manifold Dirac Operatörünün Alt Sınır Özdeğer Problemleri

Öz

Bu makalede, Kompakt Riemannian Spin altmanifold Dirac operatörünün özdeğerlerine EnergyMomentum tensörü ve onun izine bağlı olarak optimal bir alt sınır getirmek için spinorial LeviCivita konneksiyonunu EnergyMomentum tensörü ve onun izine bağlı olarak deforme ettik.  Daha sonra bu tahminleri konformal değişim metriği altında Yamabe sayısı ve altmanifoldun alanına bağlı olarak genişlettik.

Anahtar Kelimeler

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

Kaynakça

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