6 papers
Totally umbilical hypersurfaces of Spin manifolds carrying special spinor fields
Nadine Große, Roger Nakad
Under some dimension restrictions, we prove that totally umbilical hypersurfaces of Spin manifolds carrying a parallel, real or imaginary Killing spinor are of constant mean cu…
Characterization of hypersurfaces in four dimensional product spaces via two different Spin structures
Roger Nakad, Julien Roth
The Riemannian product , where denotes the -dimensional space form of constant sectional curvature $c_i \in \mathbb…
Eigenvalue Estimate for the basic Laplacian on manifolds with foliated boundary, part II
Fida El Chami, George Habib, Ola Makhoul +1
In [4], we gave a sharp lower bound for the first eigenvalue of the basic Laplacian acting on basic -forms defined on a compact manifold whose boundary is endowed with a Riemann…
Eigenvalue Estimates of the Dirac Operator and Harmonic Forms on Kähler-Einstein Manifolds
Roger Nakad, Mihaela Pilca
We establish a lower bound for the eigenvalues of the Dirac operator defined on a compact Kähler-Einstein manifold of positive scalar curvature and endowed with particular ${\rm sp…
The twisted Spin Dirac operator on Kähler submanifolds of the complex projective space
Georges Habib, Roger Nakad
In this paper, we estimate the eigenvalues of the twisted Dirac operator on Kähler submanifolds of the complex projective space and we discuss the sharpness of this estimat…
The Hijazi inequalities on complete Riemannian Spin manifolds
Roger Nakad
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 manifolds withou…