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Title: Eigenvalue Estimates in Terms of the Extrinsic Curvature
Authors: Eker, Serhan
Değirmenci, Nedim
Keywords: Spin and Spin(c) geometry
Dirac operator
Estimation of eigenvalues
Issue Date: 2021
Publisher: Springer International Publishing Ag
Abstract: 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.
ISSN: 1028-6276
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