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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Bibliographic Details
Published in:Iranian journal of science (Online) Vol. 45; no. 4; pp. 1411 - 1416
Main Authors: EKER Serhan, Değirmenci Nedim
Format: Journal Article
Language:English
Published: Shiraz Springer Nature B.V 01.08.2021
Subjects:
Curvature
Eigenvalues
Hyperspaces
Lower bounds
Mathematical analysis
Tensors
ISSN:2731-8095, 2731-8109
Online Access:Get full text
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Summary: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.
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ISSN:2731-8095
2731-8109
DOI:10.1007/s40995-021-01136-x