L’INSTITUTFOURIER DE ANNALES

manifold with non-negative curvature and horizontal positive sectional curvature, whose metric is quasi-Einstein and whose Ricci curvature vanishes in the direction of B

Then conditioning the equation appropriately we are able to apply a contraction mapping argument to reprove the existence (see Theorem 4.7) of a short-time solution to the flow

MCOWEN, Conformal metric in R2 with prescribed Gaussian curvature and positive total curvature,

It remains a challenging prob- lem to construct non-zero elements in higher homotopy groups of (moduli) spaces of positive sectional and positive Ricci curvature metrics.. APS index

Our main result is that, on the projective completion of a pluricanonical bundle over a product of Kähler–Einstein Fano manifolds with the second Betti number 1,

We think of scalar curvature as a Riemannin incarnation of mean cur- vature (1) and we search for constraints on global geometric invariants of n-spaces X with Sc(X) > 0 that

metric with parallel Lee form on each (primary) Hopf surfaces of class 1, as well as an explicit description of the corresponding Sasakian geometry, are given in Sections 2 and 3

We also prove that the Pontrjagin ring of the normal bundle can be expressed in terms of the conformal curvature.. This provides an alternative proof for the