Related papers: Stabilities of affine Legendrian submanifolds and …

In this paper we study the deformation theory of submanifolds characterized by a system of differential forms and provide a criterion for deformations of such submanifolds to be unobstructed. We apply this deformation theory to special…

In this paper we provide a second variation formula for L-minimal Lagrangian submanifolds in a pseudo-Sasakian manifold. We apply it to the case of Lorentzian-Sasakian manifolds and relate the L-stability of L-minimal Legendrians in a…

This article continues the study of moduli spaces of special Lagrangians with boundary in a Calabi--Yau manifold. The moduli space was shown to be a smooth finite-dimensional manifold in the prequel arXiv:2503.6321918. This article…

We develop a theory of stable bundles and affine Hermitian-Einstein metrics for flat vector bundles over a special affine manifold (a manifold admitting an atlas whose gluing maps are all locally constant volume-preserving affine maps). Our…

It is shown that a canonical geometric setting of the integrable TED equation is a Kahlerian tangent bundle of an affine manifold. The remarkable multi-dimensional consistency of this 4+4-dimensional dispersionless partial differential…

For a given minimal Legendrian submanifold $L$ of a Sasaki-Einstein manifold we construct two families of eigenfunctions of the Laplacian of $L$ and we give a lower bound for the dimension of the corresponding eigenspace. Moreover, in the…

Real Legendrian subvarieties are classical objects of differential geometry and classical mechanics and they have been studied since antiquity. However, complex Legendrian subvarieties are much more rigid and have more exceptional…

We introduce and discuss notions of regularity and flexibility for Lagrangian manifolds with Legendrian boundary in Weinstein domains. There is a surprising abundance of flexible Lagrangians. In turn, this leads to new constructions of…

We show that the moduli space of simple flat bundles over a compact Sasakian manifold is a finite disjoint union of moduli spaces of simple flat bundles with fixed basic structures. This gives a detailed description of the non-abelian Hodge…

By means of a Fourier-Mukai transform we embed moduli spaces of stable bundles on an algebraic curve C as isotropic subvarieties of moduli spaces of mu-stable bundles on the Jacobian variety J(C). When g(C)=2 this provides new examples of…

In this article we study Weinstein structures endowed with a Lefschetz fibration in terms of the Legendrian front projection. First we provide a systematic recipe for translating from a Weinstein Lefschetz bifibration to a Legendrian…

We study semi--algebraic domains associated with symplectic tori and conjecturally identified with spaces of stability conditions on the Fukaya categories of these tori. Our motivation is to test which results from the theory of flat…

It is proved that the moduli space of all connected compact orientable embedded minimal affine Lagrangian submanifolds of a complex equiaffine space constitutes an infinite dimensional Frechet manifold (if it is not the empty set). The…

We classify the biharmonic Legendre curves in a Sasakian space form, and obtain their explicit parametric equations in the $(2n+1)$-dimensional unit sphere endowed with the canonical and deformed Sasakian structures defined by Tanno. Then,…

Special Lagrangian submanifolds are submanifolds of a Calabi-Yau manifold calibrated by the real part of the holomorphic volume form. In this paper we use elliptic theory for edge-degenerate differential operators on singular manifolds to…

We show that every toric Sasaki-Einstein manifold $S$ admits a special Legendrian submanifold $L$ which arises as the link ${\rm fix}(\tau)\cap S$ of the fixed point set ${\rm fix}(\tau)$ of an anti-holomorphic involution $\tau$ on the cone…

We introduce a notion of stable spherical variety which includes the spherical varieties under a reductive group $G$ and their flat equivariant degenerations. Given any projective space $\bP$ where $G$ acts linearly, we construct a moduli…

This paper considers the natural geometric structure on the moduli space of deformations of a compact special Lagrangian submanifold $L^n$ of a Calabi-Yau manifold. From the work of McLean this is a smooth manifold with a natural $L^2$…

We construct proper moduli algebraic spaces of K-polystable $\mathbb{Q}$-Fano cones (a.k.a. Calabi-Yau cones) or equivalently their links i.e., Sasaki-Einstein manifolds with singularities. As a byproduct, it gives alternative algebraic…

For any subgroup of $\mathrm{SL}(3,\mathbb{R})\ltimes\mathbb{R}^3$ obtained by adding a translation part to a subgroup of $\mathrm{SL}(3,\mathbb{R})$ which is the fundamental group of a finite-volume convex projective surface, we first show…