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  • 1
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The Positive Action conjecture requires that the action of any asymptotically Euclidean 4-dimensional Riemannian metric be positive, vanishing if and only if the space is flat. Because any Ricci flat, asymptotically Euclidean metric has zero action and is local extremum of the action which is a local minimum at flat space, the conjecture requires that there are no Ricci flat asymptotically Euclidean metrics other than flat space, which would establish that flat space is the only local minimum. We prove this for metrics onR 4 and a large class of more complicated topologies and for self-dual metrics. We show that ifR μ μ ≧0 there are no bound states of the Dirac equation and discuss the relevance to possible baryon non-conserving processes mediated by gravitational instantons. We conclude that these are forbidden in the lowest stationary phase approximation. We give a detailed discussion of instantons invariant under anSU(2) orSO(3) isometry group. We find all regular solutions, none of which is asymptotically Euclidean and all of which possess a further Killing vector. In an appendix we construct an approximate self-dual metric onK3 — the only simply connected compact manifold which admits a self-dual metric.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We study the holomorphic structure of certain complex manifolds associated withW ∞ algebras, namely, the flag manifoldsW ∞/T ∞ andW 1+∞/T 1+∞, and the spacesW ∞/SL(∞),R) andW 1+∞/GL(∞,R), whereT ∞ andT 1+∞ are the maximal tori inW ∞ andW 1+∞. We compute their Ricci curvature and show how the results are related to the anomaly-freedom conditions forW ∞ andW 1+∞. We discuss the relation of these manifolds with extensions of universal Teichmüller space.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 61 (1978), S. 239-248 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We compare some of the properties of ℂP 2 with those of the SU(2) Yang-Mills Instanton and conclude that ℂP 2 may be regarded as a gravitational pseudoparticle surrounded by an event horizon.
    Type of Medium: Electronic Resource
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  • 4
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We consider compactifications of eleven-dimensional supergravity to five and three spacetime dimensions, on internal spacesK 6 andK 2×K 6, whereK n denotes ann-dimensional Kähler manifold. The compactifications to five dimensions yield no surviving spacetime supersymmetries. However, we find compactifications to three dimensions onS 2×K 6 andT 2×K 6 whereK 6 is Ricci-flat and Kähler (a Calabi-Yau space) withN=4 supersymmetry. We also discuss the massless spectrum.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 127 (1990), S. 529-553 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Starting from a 4n-dimensional quaternionic Kähler base space, we construct metrics of cohomogeneity one in (4n+3) dimensions whose level surfaces are theS 2 bundle space of almost complex structures on the base manifold. We derive the conditions on the metric functions that follow from imposing the Einstein equation, and obtain solutions both for compact and non-compact (4n+3)-dimensional spaces. Included in the non-compact solutions are two Ricci-flat 7-dimensional metrics withG 2 holonomy. We also discuss two other Ricci-flat solutions, one on theR 4 bundle overS 3 and the other on anR 4 bundle overS 4. These haveG 2 and Spin(7) holonomy respectively.
    Type of Medium: Electronic Resource
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