Eigenvalue Estimates in Terms of the Extrinsic Curvature

In this paper, we give a new lower bound for the eigenvalues of the Dirac operator defined on the Spin Riemannian hypersurface manifold endowed with 2-tensor, in terms of the Energy-Momentum tensor, scalar curvature and extrinsic curvature. Then this estimate is improved in two different ways by con...

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Vydáno v:Iranian journal of science (Online) Ročník 45; číslo 4; s. 1411 - 1416
Hlavní autoři: EKER Serhan, Değirmenci Nedim
Médium: Journal Article
Jazyk:angličtina
Vydáno: Shiraz Springer Nature B.V 01.08.2021
Témata:
Curvature
Eigenvalues
Hyperspaces
Lower bounds
Mathematical analysis
Tensors
ISSN:2731-8095, 2731-8109
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Popis
Shrnutí:In this paper, we give a new lower bound for the eigenvalues of the Dirac operator defined on the Spin Riemannian hypersurface manifold endowed with 2-tensor, in terms of the Energy-Momentum tensor, scalar curvature and extrinsic curvature. Then this estimate is improved in two different ways by considering the conformal invariance of the Dirac operator. The first is given in term of the first eigenvalue of the Yamabe operator. The latter, is given in terms of the the area of a topological 2-sphere.
Bibliografie:ObjectType-Article-1
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content type line 14
ISSN:2731-8095
2731-8109
DOI:10.1007/s40995-021-01136-x