The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “Conformal gradient vector fields on a compact Riemannian manifold”

On metrics of positive Ricci curvature conformal to M × 𝐑 m

Juan Miguel Ruiz (2009)

Archivum Mathematicum

Similarity:

Let ( M n , g ) be a closed Riemannian manifold and g E the Euclidean metric. We show that for m > 1 , M n × 𝐑 m , ( g + g E ) is not conformal to a positive Einstein manifold. Moreover, M n × 𝐑 m , ( g + g E ) is not conformal to a Riemannian manifold of positive Ricci curvature, through a radial, integrable, smooth function, ϕ : 𝐑 𝐦 → 𝐑 + , for m > 1 . These results are motivated by some recent questions on Yamabe constants.

The spectral geometry of the Weyl conformal tensor

N. Blažić, P. Gilkey, S. Nikčević, U. Simon (2005)

Banach Center Publications

Similarity:

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.