Related papers: Split Special Lagrangian Geometry

Semi-Riemannian manifolds that satisfy (homogeneous) linear differential conditions of arbitrary order on the curvature are analyzed. They include, in particular, the spaces with (higher-order) recurrent curvature, (higher-order) symmetric…

We study the hypersymplectic geometry of the moduli space of solutions to Hitchin's harmonic map equations on a $G$-bundle. This is the split-signature analogue of Hitchin's Higgs bundle moduli space. Due to the lack of definiteness, this…

Metallic structures, introduced by V. de Spinadel in 2002, opened a new avenue in differential geometry. Building upon this concept, C. E. Hre\c{t}canu and M. Crasmareanu laid the foundation for metallic Riemannian manifolds in 2013. The…

We study anomalies of non-invertible duality symmetries in both 2d and 4d, employing the tool of the Symmetry TFT. In the 2d case we rephrase the known obstruction theory for the Tambara-Yamagami fusion category in a way easily…

We describe basic concepts of noncommutative geometry and a general construction extending the familiar duality between ordinary spaces and commutative algebras to a duality between Quotient spaces and Noncommutative algebras. Basic tools…

Let $M$ be a smooth projective variety and $\mathbf{D}$ an ample normal crossings divisor. From topological data associated to the pair $(M, \mathbf{D})$, we construct, under assumptions on Gromov-Witten invariants, a series of…

This paper is devoted to the study of geometric structures modeled on homogeneous spaces G/P, where G is a real or complex semisimple Lie group and $P\subset G$ is a parabolic subgroup. We use methods from differential geometry and very…

We study the symmetries of the N=1 exactly marginal deformations of N=4 Super Yang-Mills theory. For generic values of the parameters, these deformations are known to break the SU(3) part of the R-symmetry group down to a discrete subgroup.…

Classical geometric mechanics, including the study of symmetries, Lagrangian and Hamiltonian mechanics, and the Hamilton-Jacobi theory, are founded on geometric structures such as jets, symplectic and contact ones. In this paper, we shall…

Let (M,w) be a compact symplectic 2n-manifold, and g a Riemannian metric on M compatible with w. For instance, g could be Kahler, with Kahler form w. Consider compact Lagrangian submanifolds L of M. We call L Hamiltonian stationary, or…

Over the past few years there has been considerable progress in the structural understanding of special Colombeau algebras. We present some of the main trends in this development: non-smooth differential geometry, locally convex theory of…

We discuss the local differential geometry of convex affine spheres in $\re^3$ and of minimal Lagrangian surfaces in Hermitian symmetric spaces. In each case, there is a natural metric and cubic differential holomorphic with respect to the…

Let $\pi : E\to M$ be a smooth fiber bundle whose total space is a symplectic manifold and whose fibers are Lagrangian. Let $L$ be an embedded Lagrangian submanifold of $E$. In the paper we address the following question: how can one…

This work is a galoisian study of the spectral problem $L\Psi=\lambda\Psi$, for algebro-geometric second order differential operators $L$, with coefficients in a differential field, whose field of constants $C$ is algebraically closed and…

A geometry of superspace corresponding to double field theory is developed, with type II supergravity in D=10 as the main example. The formalism is based on an orthosymplectic extension OSp(d,d|2s) of the continuous T-duality group.…

We consider harmonic maps into pseudo-Riemannian manifolds. We show the removability of isolated singularities for continuous maps, i.e. that any continuous map from an open subset of R^m into a pseudo-Riemannian manifold which is two times…

In this article, we study geometric aspects of semi-arithmetic Riemann surfaces by means of number theory and hyperbolic geometry. First, we show the existence of infinitely many semi-arithmetic Riemann surfaces of various shapes and prove…

Optimal transport and information geometry both study geometric structures on spaces of probability distributions. Optimal transport characterizes the cost-minimizing movement from one distribution to another, while information geometry…

It is well-known that a Lagrangian induces a compatible presymplectic form on the equation manifold (stationary surface, understood as a submanifold of the respective jet-space). Given an equation manifold and a compatible presymplectic…

In the last two decades, one of the most important developments in Riemannian geometry is the collapsing theory of Cheeger-Fukaya-Gromov. A Riemannian manifold is called (sufficiently) collapsed if its dimension looks smaller than its…