We give a natural way to identify between two scales, potentially arbitrarily far apart, in non-compact Ricci-flat manifold with Euclidean volume growth when tangent cone at infinity has smooth cross section. The identification map is given as the gradient flow of solution an elliptic equation.

We show that the Ricci flat Calabi's metrics on holomorphic line bundles over compact Kähler--Einstein manifolds are not projectively induced. As a byproduct we solve conjecture addressed in [10] by proving any multiple of Eguchi-Hanson metric blow-up $\mathbb{C}^2$ at origin is

Starting from compact symmetric spaces of inner type, we provide infinite families homogeneous carrying invariant non-flat Bismut connections with vanishing Ricci tensor. These examples turn out to be generalized order [Formula: see text] and (up coverings) they can realized as minimal submanifolds the flat model spaces, namely Lie groups. This construction generalizes standard Cartan embedding...

We calculate the metric on the D-brane vacuum moduli space for backgrounds of the form C 3 /Γ for cyclic groups Γ. In the simplest procedure — starting with a flat " seed " metric on the covering space — we find that the resulting D-brane metric is not Ricci-flat. We argue that this is likely to be true of the true 0-brane metric at weak string coupling.

We show (a) that any entire graphic self-shrinking solution to the Lagrangian mean curvature flow in C with the Euclidean metric is flat; (b) that any space-like entire graphic self-shrinking solution to the Lagrangian mean curvature flow in C with the pseudo-Euclidean metric is flat if the Hessian of the potential is bounded below quadratically; and (c) the Hermitian counterpart of (b) for the...

We prove that a Kähler supermetric on a supermanifold with one complex fermionic dimension admits a super Ricci-flat supermetric if and only if the bosonic metric has vanishing scalar curvature. As a corollary, it follows that Yau’s theorem does not hold for supermanifolds. Calabi[1] proposed that if a Kähler manifold has vanishing first Chern class, that is, the Ricci-form obeys Rij̄(g) = ∂iv̄j ...