Related papers: Special Lagrangian submanifolds in the complex sph…
We present a classification of all spherical indecomposable representations of classical and exceptional Lie superalgebras. We also include information about stabilizers, symmetric algebras, and Borels for which sphericity is achieved. In…
We classify the Lagrangian orientable surfaces in complex space forms with the property that the ellipse of curvature is always a circle. As a consequence, we obtain new characterizations of the Clifford torus of the complex projective…
We clarify the recently proposed method to compute a Special K\"ahler metric on a Calabi-Yau complex structures moduli space that uses the fact that the moduli space is a subspace of specific Frobenius manifold. We apply this method to…
In this paper the notion of a superconformal structure on a supermanifold is introduced in an effort to study the superparticle sigma-model. There are, in particular, two main aspects of the sigma-model which are investigated. The first is…
In this paper we give a construction of Lagrangian torus fibration for Calabi-Yau hypersurface in toric variety via the method of gradient flow. Using our construction of Lagrangian torus fibration, we are able to prove the symplectic…
We exhibit a transformation taking special Lagrangian submanifolds of a Calabi-Yau together with local systems to vector bundles over the mirror manifold with connections obeying deformed Hermitian-Yang-Mills equations. That is, the…
This is the fourth in a series of five papers math.DG/0211294, math.DG/0211295, math.DG/0302355, math.DG/0303272 studying compact special Lagrangian submanifolds (SL m-folds) X in (almost) Calabi-Yau m-folds M with singularities x_1,...,x_n…
Manifold submetries of the round sphere are a class of partitions of the round sphere that generalizes both singular Riemannian foliations, and the orbit decompositions by the orthogonal representations of compact groups. We exhibit a…
We consider Open Gromov-Witten invariants for noncompact Calabi-Yau in the case the Lagrangian has the topology of $\R^2 \times S^1$. The definition of the invariant involves the choice of a frame for the Lagrangian, in accord with string…
We derive in the SCFT and low energy effective action frameworks the necessary and sufficient conditions for supersymmetric cycles in exceptional holonomy manifolds and Calabi-Yau 4-folds. We show that the Cayley cycles in $Spin(7)$…
Calabi--Yau manifolds have risen to prominence in algebraic geometry, in part because of mirror symmetry and enumerative geometry. After Bershadsky--Cecotti--Ooguri--Vafa (BCOV), it is expected that genus 1 curve counting on a Calabi--Yau…
We fully classify all Lagrangian submanifolds of a complex Grassmannian which are an orbit of a compact group of isometries and have positive Euler characteristic.
We study a large class of Poisson manifolds, derived from Manin triples, for which we construct explicit partitions into regular Poisson submanifolds by intersecting certain group orbits. Examples include all varieties ${\mathcal L}$ of…
In this paper we describe the algebra of differential invariants for GL(n,C)-structures. This leads to classification of almost complex structures of general positions. The invariants are applied to the existence problem of…
We continue the study of the Strominger-Yau-Zaslow mirror symmetry conjecture. Roughly put, this states that if two Calabi-Yau manifolds X and Y are mirror partners, then X and Y have special Lagrangian torus fibrations which are dual to…
We construct new examples of special Lagrangian submanifolds $Y\subset \mathbf{C}^{n+1}$, $n\geq 3$ in a neighborhood of the origin, with an isolated singularity, but with cylindrical tangent cone $C\times\mathbf{R}$. Moreover,…
We study modules over the algebroid stack $\W[\stx]$ of deformation quantization on a complex symplectic manifold $\stx$ and recall some results: construction of an algebra for $\star$-products, existence of (twisted) simple modules along…
We show that the formal moduli space of a Calabi-Yau manifold $X^n$ carries a linear structure, as predicted by mirror symmetry. This linear structure is canonically associated to a splitting of the Hodge filtration on $H^n(X)$.
In the framework of special Kahler geometry we consider the supergravity-matter system which emerges on a K3-fibered Calabi-Yau manifold. By applying the rigid limit procedure in the vicinity of a conifold singularity we compute the Kahler…
We propose a general theory of the Open Gromov-Witten invariant on Calabi-Yau three-folds. We introduce the moduli space of multi-curves and show how it leads to invariants. Our construction is based on an idea of Witten. In the special…