Related papers: A rigidity theorem for Lagrangian deformations

In this survey on local additive invariants of real and complex definable singular germs we systematically present classical or more recent invariants of different nature as emerging from a tame degeneracy principle. For this goal, we…

We describe isotropic orbits for the restricted action of a subgroup of a Lie group acting on a symplectic manifold by Hamiltonian symplectomorphisms and admitting an Ad*-equivariant moment map. We obtain examples of Lagrangian orbits of…

In this paper we survey some finiteness results of the deformation classes of hyperk\"ahler Lagrangian fibrations, and we prove finiteness for stable Lagrangian fibrations with a given discriminant divisor.

We introduce new pseudo-metrics on spaces of Lagrangian submanifolds of a symplectic manifold $(M,\omega)$ by considering areas associated to projecting Lagrangian cobordisms in $\mathbb{C} \times M$ to the "time-energy plane" $\mathbb{C}$.…

We determine all tight Lagrangian surfaces in $S^2 \times S^2$. In particular, globally tight Lagrangian surfaces in $S^2 \times S^2$ are nothing but real forms.

We study collections of exact Lagrangian submanifolds respecting some uniform Riemannian bounds, which we equip with a metric naturally arising in symplectic topology (e.g. the Lagrangian Hofer metric or the spectral metric). We exhibit…

We investigate deformations of the Kerr-(A)dS near horizon geometry and derive partial infinitesimal rigidity results for it. The proof comprises two parts. First, we follow the analysis of Jezierski and Kami\'nski [Gen Rel Grav 45 (2013)…

In this paper we first give a Bonnet theorem for conformal Lagrangian surfaces in complex space forms, then we show that any compact Lagrangian surface in the complex space form admits at most one other global isometric Lagrangian surface…

In this paper, we first introduce the concept of $\xi $-submanifold which is a natural generalization of self-shrinkers for the mean curvature flow and also an extension of $\lambda$-hypersurfaces to the higher codimension. Then, as the…

We prove that any symplectic automorphism of finite order of an irreducible holomorphic symplectic manifold of O'Grady's 10-dimensional deformation type is trivial.

We first give a deformation theory of integrable distributions of codimension 1. We define a parametrization of families of smooth hypersurfaces near a Levi flat hypersurface L such that the Levi flat deformations are given by the solutions…

Let Y be a compact reduced subspace of a complex manifold X, and let F be a subsheaf of the tangent bundle T_X which is closed under the Lie bracket. This paper discusses criteria to guarantee that infinitesimal deformations of the…

This paper develops a symplectic bifurcation theory for integrable systems in dimension four. We prove that if an integrable system has no hyperbolic singularities and its bifurcation diagram has no vertical tangencies, then the fibers of…

Lagrangian multiform theory is a variational framework for integrable systems. In this article we introduce a new formulation which is based on symplectic geometry and which treats position, momentum and time coordinates of a…

In the first section we recall some basic notions on Lie algebras. In a second time we study the algebraic variety of complex $n$-dimensional Lie algebras. We present different notions of deformations : Gerstenhaber deformations,…

Every algebraic variety can be regarded as a symplectic manifold being equipped with a Kahler form. Therefore it is natural to study lagrangian geometry of any algebraic variety. We present two basic constructions which can be applied to a…

We introduce a notion of elliptic differential graded Lie algebra. The class of elliptic algebras contains such examples as the algebra of differential forms with values in endomorphisms of a flat vector bundle over a compact manifold, etc.…

We study real Lagrangian analytic surfaces in C^2 with a non-degenerate complex tangent. Webster proved that all such surfaces can be transformed into a quadratic surface by formal symplectic transformations of C^2. We show that there is a…

We give a necessary and sufficient condition for lagrangians in a symplectic vector bundle to be deformed stably into transversal lagrangians. In the case of three lagrangians, we show that the associated Grothendieck group can be…

This is an addendum to the paper ``Deformation of $L_\infty$-Algebras'' of the same author. We explain in which way the deformation theory of $L_\infty$-algebras extends the deformation theory of singularities. We show that the construction…