A conformally invariant sphere theorem in four dimensions

Sun-Yung A. Chang; Matthew J. Gursky; Paul C. Yang

Displaying similar documents to “A conformally invariant sphere theorem in four dimensions”

Future directions of research in geometry: a summary of the panel discussion at the 2007 midwest geometry conference.

Peterson, Lawrence J. (ed.) (2007)

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

Similarity:

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.

On conformally recurrent Ricci-recurrent manifolds

W. Roter (1982)

Colloquium Mathematicae

Similarity:

Constant scalar curvature metrics on connected sums.

Joyce, Dominic (2003)

International Journal of Mathematics and Mathematical Sciences

Similarity:

On metrics of positive Ricci curvature conformal to $M \times 𝐑^{m}$

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 $m > 1$ , $(M^{n} \times 𝐑^{m}, (g + g_{E}))$ is not conformal to a positive Einstein manifold. Moreover, $(M^{n} \times 𝐑^{m}, (g + g_{E}))$ is not conformal to a Riemannian manifold of positive Ricci curvature, through a radial, integrable, smooth function, $ϕ : 𝐑^{𝐦} \to 𝐑^{+}$ , for $m > 1$ . These results are motivated by some recent questions on Yamabe constants.