Conformal metrics with constant -curvature.
Malchiodi, Andrea (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Malchiodi, Andrea (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Chang, Sun-Yung A., Qing, Jie, Yang, Paul (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Sharief Deshmukh, Falleh Al-Solamy (2008)
Colloquium Mathematicae
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It is proved that if an n-dimensional compact connected Riemannian manifold (M,g) with Ricci curvature Ric satisfying 0 < Ric ≤ (n-1)(2-nc/λ₁)c for a constant c admits a nonzero conformal gradient vector field, then it is isometric to Sⁿ(c), where λ₁ is the first nonzero eigenvalue of the Laplacian operator on M. Also, it is observed that existence of a nonzero conformal gradient vector field on an n-dimensional compact connected Einstein manifold...
Peterson, Lawrence J. (ed.) (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Novica Blažić (2005)
Kragujevac Journal of Mathematics
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Branson, Thomas P. (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Joyce, Dominic (2003)
International Journal of Mathematics and Mathematical Sciences
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Begewadi, C.S., Kumar, E.Girish, Venkatesha (2005)
Novi Sad Journal of Mathematics
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Paneitz, Stephen M. (2008)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Matthias Fischmann (2014)
Archivum Mathematicum
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The well known conformal covariance of the Dirac operator acting on spinor fields does not extend to its powers in general. For odd powers of the Dirac operator we derive an algorithmic construction in terms of associated tractor bundles computing correction terms in order to achieve conformal covariance. These operators turn out to be formally (anti-) self-adjoint. Working out this algorithm we recover explicit formula for the conformal third and present a conformal fifth power of the...
Eastwood, Michael G., Gover, A.Rod (2008)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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N. Blažić, P. Gilkey, S. Nikčević, U. Simon (2005)
Banach Center Publications
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We study when the Jacobi operator associated to the Weyl conformal curvature tensor has constant eigenvalues on the bundle of unit spacelike or timelike tangent vectors. This leads to questions in the conformal geometry of pseudo-Riemannian manifolds which generalize the Osserman conjecture to this setting. We also study similar questions related to the skew-symmetric curvature operator defined by the Weyl conformal curvature tensor.