scholarly journals Complex contact structures and the first eigenvalue of the dirac operator on Kähler manifolds

1995 ◽  
Vol 5 (3) ◽  
pp. 604-618 ◽  
Author(s):  
K. -D. Kirchberg ◽  
U. Semmelmann
Keyword(s):  
Dirac Operator ◽  
Kähler Manifolds ◽  
Contact Structures ◽  
Kahler Manifolds ◽  
First Eigenvalue ◽  
The First Eigenvalue

scholarly journals A Lichnerowicz estimate for the first eigenvalue of convex domains in Kähler manifolds

2013 ◽  
Vol 6 (5) ◽  
pp. 1001-1012
Author(s):  
Vincent Guedj ◽  
Boris Kolev ◽  
Nader Yeganefar
Keyword(s):  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
First Eigenvalue ◽  
Convex Domains ◽  
The First Eigenvalue

scholarly journals THE FIRST EIGENVALUE OF THE DIRAC OPERATOR IN A CONFORMAL CLASS

2006 ◽  
Vol 03 (05n06) ◽  
pp. 833-844 ◽  
Author(s):  
BERND AMMANN ◽  
EMMANUEL HUMBERT
Keyword(s):  
Dirac Operator ◽  
Variational Problem ◽  
Mean Curvature ◽  
Unit Volume ◽  
Constant Mean Curvature ◽  
Positive Eigenvalue ◽  
First Eigenvalue ◽  
Conformal Class ◽  
Open Problems ◽  
The First Eigenvalue

In this overview article, we study the first positive eigenvalue of the Dirac operator in a unit volume conformal class. In particular, we discuss the question whether the infimum is attained. In the first part, we explain the corresponding variational problem. In the following parts we discuss the relation to the spinorial mass endomorphism and an application to surfaces of constant mean curvature. The article also mentions some open problems and work in progress.

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