45 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
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in prescribed directions.Comment: This paper has been withdrawn by the author.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
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
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 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
Hybrid functions approach to solve 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 key point is to derive a new
approximation for the derivatives of the solutions and then reduce the
integro-differential equation to a system of algebraic equations that can be
solved using classical methods. Some numerical examples are dedicated for
showing efficiency and validity of the method that we introduce
Characterization of hypersurfaces in four dimensional product spaces via two different Spin^c structures
The Riemannian product M1(c1)×M2(c2), where Mi(ci) denotes the 2-dimensional space form of constant sectional curvature ci ∈ R, has two different Spin c structures carrying each a parallel spinor. The restriction of these two parallel spinor fields to a 3-dimensional hypersurface M characterizes the isometric immersion of M into M1(c1) × M2(c2). As an application, we prove that totally umbilical hypersurfaces of M1(c1) × M1(c1) and totally umbilical hypersurfaces of M1(c1) × M2(c2) (c1 = c2) having a local structure product, are of constant mean curvature