252 research outputs found
The Hijazi inequalities on complete Riemannian Spin 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 manifolds without boundary and of finite volume. Under some
additional assumptions, using the refined Kato inequality, we prove the Hijazi
type inequality for elements of the essential spectrum. The limiting cases are
also studied
Boundary value problems for noncompact boundaries of Spinᶜ manifolds and spectral estimates
We study boundary value problems for the Dirac operator on Riemannian
Spin manifolds of bounded geometry and with noncompact boundary. This
generalizes a part of the theory of boundary value problems by C. B\"ar and W.
Ballmann for complete manifolds with closed boundary. As an application, we
derive the lower bound of Hijazi-Montiel-Zhang, involving the mean curvature of
the boundary, for the spectrum of the Dirac operator on the noncompact boundary
of a Spin manifold. The limiting case is then studied and examples are then
given.Comment: Accepted in Proceedings of the London Mathematical Societ
Spinorial Characterization of CR Structures, I
We characterize certain CR structures of arbitrary codimension (different
from 3, 4 and 5) on Riemannian Spin manifolds by the existence of a
Spin structure carrying a strictly partially pure spinor field.
Furthermore, we study the geometry of Riemannian Spin manifolds carrying a
strictly partially pure spinor which satisfies the generalized Killing equation
in prescribed directions.Comment: This paper has been withdrawn by the author. All results have been
changed because we extended them to all co-dimensions. We changed completely
the pape
Hypersurfaces of Spin manifolds and Lawson type correspondence
Simply connected 3-dimensional homogeneous manifolds , with
4-dimensional isometry group, have a canonical Spin structure carrying
parallel or Killing spinors. The restriction to any hypersurface of these
parallel or Killing spinors allows to characterize isometric immersions of
surfaces into . As application, we get an elementary proof of
a Lawson type correspondence for constant mean curvature surfaces in . Real hypersurfaces of the complex projective space and the complex
hyperbolic space are also characterized via Spin spinors.Comment: to appear in Annals of Global Analysis and Geometry (AGAG
Eigenvalue Estimates of the Dirac Operator and Harmonic Forms on K\"ahler-Einstein Manifolds
We establish a lower bound for the eigenvalues of the Dirac operator defined
on a compact K\"ahler-Einstein manifold of positive scalar curvature and
endowed with particular structures. The limiting case is
characterized by the existence of K\"ahlerian Killing spinors in
a certain subbundle of the spinor bundle. Moreover, we show that the Clifford
multiplication between an effective harmonic form and a K\"ahlerian Killing
spinor field vanishes. This extends to the case
the result of A. Moroianu stating that, on a compact K\"ahler-Einstein manifold
of complex dimension carrying a complex contact structure, the
Clifford multiplication between an effective harmonic form and a K\"ahlerian
Killing spinor is zero
Complex and Lagrangian surfaces of the complex projective plane via K\"ahlerian Killing Spin spinors
The complex projective space of complex dimension has a
Spin structure carrying K\"ahlerian Killing spinors. The restriction of one
of these K\"ahlerian Killing spinors to a surface characterizes the
isometric immersion of into if the immersion is either
Lagrangian or complex.Comment: 18 page
Complex Generalized Killing Spinors on Riemannian Spin manifolds
In this paper, we extend the study of generalized Killing spinors on
Riemannian Spin manifolds started by Moroianu and Herzlich to complex
Killing functions. We prove that such spinor fields are always real Spin
Killing spinors or imaginary generalized Spin Killing spinors, providing
that the dimension of the manifold is greater or equal to 4. Moreover, we
classify Riemannian Spin manifolds carrying imaginary and imaginary
generalized Killing spinors.Comment: 15 page
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