10 research outputs found
The First Eigenvalue of the Dirac Operator on Compact Spin Symmetric Spaces
We give a formula for the first eigenvalue of the Dirac operator acting on
spinor fields of a spin compact irreducible symmetric space
The First Eigenvalue of the Dirac Operator on Compact Outer Spin Symmetric Spaces
In two previous papers, we started a study of the first eigenvalue of the Dirac operator on compact spin symmetric spaces, providing, for symmetric spaces of "inner" type, a formula giving this first eigenvalue in terms of the algebraic data of the groups involved. We conclude here that study by giving the explicit expression of the first eigenvalue for "outer" compact spin symmetric spaces
A formula for the First Eigenvalue of the Dirac Operator on Compact Spin Symmetric Spaces
Let be a simply connected spin compact inner irreducible symmetric
space, endowed with the metric induced by the Killing form of sign-changed.
We give a formula for the square of the first eigenvalue of the Dirac operator
in terms of a root system of . As an example of application, we give the
list of the first eigenvalues for the spin compact irreducible symmetric spaces
endowed with a quaternion-K\"{a}hler structure
The First Eigenvalue of the Dirac Operator on Compact Outer Spin Symmetric Spaces
In two previous papers, we started a study of the first eigenvalue of the Dirac operator on compact spin symmetric spaces, providing, for symmetric spaces of "inner" type, a formula giving this first eigenvalue in terms of the algebraic data of the groups involved. We conclude here that study by giving the explicit expression of the first eigenvalue for "outer" compact spin symmetric spaces
Sur les connexions conformes
SIGLECNRS T 59346 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc
A spinorial approach to Riemannian and conformal geometry
International audienceThe book aims to give an elementary and comprehensive introduction to Spin Geometry, with particular emphasis on the Dirac operator which plays a fundamental rôle in Differential Geometry and Mathematical Physics.After a self-contained presentation of the basic algebraic, geometrical, analytical and topological ingredients, a systematic study of the spectral properties of the Dirac operator on compact spin manifolds is carried out. The classical estimates on eigenvalues and their limiting cases are discussed next, highlighting the subtle interplay of spinors and special geometric structures.Several applications of these ideas are presented, including spinorial proofs of the Positive Mass Theorem or the classification of positive Kähler-Einstein contact manifolds. Representation theory is used to explicitly compute the Dirac spectrum of compact symmetric spaces.The special features of the book include a unified treatment of spin^c and conformal spin geometry (with special emphasis on the conformal covariance of the Dirac operator), an original introduction to pseudodifferential calculus, a spinorial characterization of special geometries, and a self-contained presentation of the representation-theoretical tools needed in order to apprehend spinors.We hope that this book will help advanced graduate students and researchers to get more familiar with this beautiful, though not sufficiently known, domain of mathematics with great relevance to both theoretical physics and geometry