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Displaying similar documents to “Conformal Jacobi operators of hypersurfaces in the de Sitter space.”

The spectral geometry of the Weyl conformal tensor

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.

Conformal gradient vector fields on a compact Riemannian manifold

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...

On Gauss-Bonnet curvatures.

Labbi, Mohammed-Larbi (2007)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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