Supersymmetric nonlinear sigma models are obtained from linear sigma models by imposing supersymmetric constraints. If we introduce auxiliary chiral and vector superfields, these constraints are expressed by D-terms and F-terms depending on the target manifolds. Auxiliary vector superfields appears as gauge fields without kinetic terms. If there is no D-term constraints, the target manifolds ar...

Abstract Let π −→ X be a principal elliptic fibration over a Kähler base X . We assume that the Kähler form on X is lifted to an exact form on M (such fibrations are called positive). Examples of these are regular Vaisman manifolds (in particular, the regular Hopf manifolds) and Calabi-Eckmann manifolds. Assume that dimM > 2. Using the KobayashiHitchin correspondence, we prove that all stable b...

We consider systems of Ito’s stochastic differential equations with smooth compact invariant manifolds. The problem addressed is an exponential mean square (EMS) stabilization of these manifolds. The necessary and sufficient conditions of the stabilizability are derived on the base of the spectral criterion of the EMS-stability of invariant manifolds. We suggest methods for the design of the fe...

In this note we introduce Thorn classes of microbundles. We determine the Thorn class of the Whitney sum as the cup product of Thorn classes and state two applications ; one to Gysin sequences of Whitney sums and one to the Atiyah-Bott-Shapiro duality theorem for Thorn spaces (cf. Atiyah [2]). Thus our main result states tha t for microbundles /xi, JU2 over a compact (topological) manifold X, i...

We formulate a conjecture that arithmetic locally symmetric manifolds have simple homotopy type, and prove it for the non-compact case. More precisely, we show that, for any symmetric space S of noncompact type without Euclidean de Rham factors, there are constants α = α(S) and d = d(S) such that any non-compact arithmetic manifold, locally isometric to S, is homotopically equivalent to a simpl...

We prove a conjecture of Artur Elezi [4] in a generalized form suggested by Givental [5]. Namely, our main result relates genus-0 Gromov–Witten invariants of a bundle space with such invariants of the base, provided that the fiber is a toric manifold. When the base is the point, a new proof of mirror theorems by A. Givental [6] and H. Iritani [9] for toric manifolds is obtained. 1 Formulations ...

In this paper, we obtain lower bounds for the BrownYork quasilocal mass and the Bartnik quasilocal mass for compact three manifolds with smooth boundaries. As a consequence, we derive sufficient conditions for the existence of horizons for a certain class of compact manifolds with boundary and some asymptotically flat complete manifolds. The method is based on analyzing Hawking mass and inverse...

A new class of compact Kähler manifolds, called special, is defined: they are the ones having no fibration with base an orbifold of general type, the orbifold structure on the base being defined by the multiple fibres of the fibration (see §1). The special manifolds are in many respect higher-dimensional generalisations of rational and elliptic curves. For example, we show that being rationally...

where k is the first Betti number b^M), T is a flat riemannian λ -torus, M~ is a compact connected Ricci-flat (n — λ;)-manifold, and Ψ is a finite group of fixed point free isometries of T x M' of a certain sort (Theorem 4.1). This extends Calabi's result on the structure of compact euclidean space forms ([7] see [20, p. 125]) from flat manifolds to Ricci-flat manifolds. We use it to essentiall...