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  • 1
    Electronic Resource
    Electronic Resource
    Quaternionic Killing Spinors (1998)
    Springer
    Annals of global analysis and geometry 16 (1998), S. 63-87 
    Details
    ISSN: 1572-9060
    Keywords: Dirac operator ; Killing spinor ; quaternionic Kähler manifold
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In [17] we proved a lower bound for the spectrum of the Dirac operator on quaternionic Kähler manifolds. In the present article we study the limiting case, i.e. manifolds where the lower bound is attained as an eigenvalue. We give an equivalent formulation in terms of a quaternionic Killing equation and show that the only symmetric quaternionic Kähler manifolds with smallest possible eigenvalue are the quaternionic projective spaces.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006545828324
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Complex contact structures and the first eigenvalue of the dirac operator on Kähler manifolds (1995)
    Springer
    Geometric and functional analysis 5 (1995), S. 604-618 
    Details
    ISSN: 1420-8970
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper Kählerian Killing spinors on manifolds of complex dimensionm=4l+3 are constructed. The construction is based on a theorem which states that a closed Kähler Einstein manifold of complex dimension 4l+3 and positive scalar curvature admits a Kählerian Killing spinor if and only if there is a complex (2l+1)-contact structure. In particular, any complex contact structure in the usual sense gives rise to such a generalized contact structure. Using this, new examples of Kählerian Killing spinors are obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01895834
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  • 3
    Electronic Resource
    Electronic Resource
    The First Eigenvalue of the Dirac Operator on Quaternionic Kähler Manifolds (1998)
    Springer
    Communications in mathematical physics 199 (1998), S. 327-349 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract: In [15] we proved a lower bound for the spectrum of the Dirac operator on quaternionic Kähler manifolds. In the present article we show that the only manifolds in the limit case, i.–e. the only manifolds where the lower bound is attained as an eigenvalue, are the quaternionic projective spaces. We use the equivalent formulation in terms of the quaternionic Killing equation introduced in [16] and show that a nontrivial solution defines a parallel spinor on the associated hyperkähler manifold.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002200050504
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Eigenvalue estimates for the Dirac operator on quaternionic Kähler manifolds (1999)
    Springer
    Mathematische Zeitschrift 230 (1999), S. 727-751 
    Details
    ISSN: 0025-5874
    Keywords: Mathematics Subject Classification (1991): 53C25, 58G25
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract. We consider the Dirac operator on compact quaternionic Kähler manifolds and prove a lower bound for the spectrum. This estimate is sharp since it is the first eigenvalue of the Dirac operator on the quaternionic projective space.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00004715
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    Paper (German National Licenses)
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