In this paper we construct a special geometry over the moduli space of type II string vacua with both NS and RR fluxes turning on. Depending on what fluxes are turning on we divide into three cases of moduli space of generalized structures. They are respectively generalized Calabi-Yau structures, generalized Calabi-Yau metric structures and N = 1 generalized string vacua. It is found that the d...

It is a classical fact that the cotangent bundle T M of a differentiable manifold M enjoys a canonical symplectic form Ω. If (M, J, g, ω) is a pseudo-Kähler or para-Kähler 2n-dimensional manifold, we prove that the tangent bundle TM also enjoys a natural pseudo-Kähler or para-Kähler structure (J̃, g̃,Ω), where Ω is the pull-back by g of Ω and g̃ is a pseudoRiemannian metric with neutral signature ...

To illustrate what this paper is about we first consider a classical example of a translation surface. Consider two copies of a regular Euclidean pentagon as on the left of figure 1. Identifying opposite parallel sides by translations one obtains a Riemann surface with a natural locally flat metric with one cone type point of total angle 6π. Since this is a compact Riemann surface it is also an...

This paper relates the boundary term in the Chern-Gauss-Bonnet formula on 4-manifolds M with the renormalized volume V , as defined in the AdS/CFT correspondence, for asymptotically hyperbolic Einstein metrics on M . In addition we show that the differential or variation dV of V , or equivalently the variation of the L norm of the Weyl curvature, is intrinsically determined by the conformal inf...

A Lagrangian formulation of the BRST quantization of generic gauge theories in general irreducible non-Abelian hypergauges is proposed on the basis of the multilevel Batalin–Tyutin formalism and a special BV–BFV dual description of a reducible gauge model on the symplectic supermanifold M0 locally parameterized by the antifields for Lagrangian multipliers and the fields of the BV method. The qu...

A φ-exponential distribution is a generalization of an exponential distribution associated to functions φ in an appropriate class, and the space of φ-exponential distributions has a dually flat structure. We study features of the space of φexponential distributions, such as the convexity in Wasserstein geometry and the stability under an evolution equation. From this study, we provide the new c...

In this article, we construct non-compact complete Einstein metrics on two infinite series of manifolds. The first manifolds are vector bundles with $\mathbb{S}^{4m+3}$ as principal orbit and $\mathbb{HP}^{m}$ singular orbit. second $\mathbb{R}^{4m+4}$ the same For each case, a continuous 1-parameter family Ricci-flat 2-parameter negative constructed. particular, $\mathrm{Spin}(7)$ $\mathbb{A}_...

We present an extension of the Gromov-Hausdorff metric on the set of compact metric spaces: the Gromov-Hausdorff-Prokhorov metric on the set of compact metric spaces endowed with a finite measure. We then extend it to the non-compact case by describing a metric on the set of rooted complete locally compact length spaces endowed with a locally finite measure. We prove that this space with the ex...

This article is devoted to a study of flat orbifold vector bundles. We construct bijection between the isomorphic classes proper bundles and equivalence representations fundamental groups base orbifolds. establish Bismut-Zhang like anomaly formula for Ray-Singer metric on determine line cohomology compact with coefficients in an bundle. show that analytic torsion acyclic unitary bundle equal va...