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Boundary value problems for noncompact boundaries of Spinc manifolds and spectral estimates
We study boundary value problems for the Dirac operator on Riemannian Spin$^c$ manifolds of bounded geometry and with noncompact boundary. This generalizes a part of the theory of boundary valueExpand
Lower Bounds for the Eigenvalues of the Dirac Operator on Spin c Manifolds
In this paper, we extend the Hijazi inequality, involving the Energy-Momentum tensor, for the eigenvalues of the Dirac operator on Spin c manifolds without boundary. The limiting case is then studiedExpand
Special submanifolds of Spin$^c$ manifolds
In this thesis, we aim to make use of Spin$^c$ geometry to study special submanifolds. We start by establishing basic results for the Spin$^c$ Dirac operator. We give then inequalities of Hijazi typeExpand
Hypersurfaces of Spinc Manifolds and Lawson Type Correspondence
Simply connected three-dimensional homogeneous manifolds $${\mathbb{E}(\kappa, \tau)}$$, with four-dimensional isometry group, have a canonical Spinc structure carrying parallel or Killing spinors.Expand
Eigenvalue estimate for the basic Laplacian on manifolds with foliated boundary
On a compact Riemannian manifold whose boundary is endowed with a Riemannian flow, we give a sharp lower bound for the first eigenvalue of the basic Laplacian acting on basic 1-forms. The equalityExpand
The Energy-Momentum Tensor on Spin Manifolds
On Spin manifolds, we study the Energy-Momentum tensor associated with a spinor field. First, we give a spinorial Gauss type formula for oriented hypersurfaces of a Spin manifold. Using the notion ofExpand
The Hijazi inequalities on complete Riemannian Spin c manifolds
In this paper, we extend the Hijazi type inequality, involving the Energy-Momentum tensor, to the eigenvalues of the Dirac operator on complete Riemannian Spin c manifolds without boundary and ofExpand
The Spin$^c$ Dirac Operator on Hypersurfaces and Applications
We extend to the eigenvalues of the hypersurface Spin$^c$ Dirac operator well known lower and upper bounds. Examples of limiting cases are then given. Futhermore, we prove a correspondence betweenExpand
The twisted Spin c Dirac operator on Kahler submanifolds of the complex projective space
Abstract In this paper, we estimate the eigenvalues of the twisted Dirac operator on Kahler submanifolds of the complex projective space C P m and we discuss the sharpness of this estimate for theExpand
A Hybrid Function Approach to Solving a Class of Fredholm and Volterra Integro-Differential Equations
In this paper, we use a numerical method that involves hybrid and block-pulse functions to approximate solutions of systems of a class of Fredholm and Volterra integro-differential equations. The keyExpand
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