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

Yıl 2020, Cilt: 13 Sayı: ÖZEL SAYI I, 56 - 62, 28.02.2020

Serhan Eker

https://doi.org/10.18185/erzifbed.605220

Cited By: 5

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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