We give a complete description of the vertex algebra global sections chiral de Rham complex an arbitrary compact Ricci-flat K\"ahler manifold.

A smooth closed manifold M is called almost Ricci-flat if $$\begin{aligned} \inf _g||\text {Ric}_g||_\infty \cdot \text {diam}_g(M)^2=0 \end{aligned}$$ where $$\text {Ric}_g$$ and {diam}_g$$ , respectively, denote the Ricci tensor diameter of g runs over all Riemannian metrics on M. By using Kummer-type method, we construct a nonspin 5-manifold which simply connected. It minimal volume vanishes...

A bstract Superstring/M-theory compactified on compact Ricci flat manifolds have recently been conjectured to exhibit instabilities whenever the metrics do not special holonomy. We use worldsheet conformal field theory investigate of Type II superstring theories compact, flat, spin 3-manifolds including a description their structures. The are signalled by appearance stringy tachyons at small ra...

A generalized metric on a manifold M M , i.e., pair alttext="left-parenthesis g comma upper H right-parenthesis"> <mml:mo str...

We present the Ricci-flat metric and its Kähler potential on the conifold with theO(N) isometry, whose conical singularity is repaired by the complex quadric surfaceQ = SO(N)/SO(N− 2)× U(1). ∗ E-mail: [email protected] † E-mail: [email protected] ‡ E-mail: [email protected] Introduction. Conformally invariant nonlinear sigma models withN = 2 supers...

‎In this paper we first obtain the non-Riemannian Randers metrics of Douglas type on two-step homogeneous nilmanifolds of dimension five‎. ‎Then we explicitly give the flag curvature formulae and the $S$-curvature formulae for the Randers metrics of Douglas type on these spaces‎. ‎Moreover‎, ‎we prove that the only simply connected five-dimensional two-step homogeneous Randers nilmanifolds of D...

Abstract We show that the singularities of twisted Kähler–Einstein metric arising as longtime solution Kähler–Ricci flow or in collapsed limit Ricci-flat Kähler metrics are intimately related to holomorphic sectional curvature reference conical geometry. This provides an alternative proof second-order estimate obtained by Gross, Tosatti, and Zhang (2020, Preprint, arXiv:1911.07315) with explici...

We present a simple derivation of the Ricci-flat Kähler metric and its Kähler potential on the canonical line bundle over arbitrary Kähler coset space equipped with the Kähler-Einstein metric. ∗ E-mail: [email protected] † E-mail: [email protected] ‡ E-mail: [email protected]