Related papers: On Indefinite Special Lagrangian Submanifolds in I…
3-dimensional Harvey Lawson submanifolds were introduced in an earlier paper by Akbulut-Salur, as examples of Lagrangian-type manifolds inside G2 manifold. In this paper, we first show that the space of deformations of a smooth, compact,…
The branched deformations of immersed compact special Lagrangian submanifolds are studied in this paper. If there exists a nondegenerate $\mathbb{Z}_2$ harmonic 1-form over a special Lagrangian submanifold $L$, we construct a family of…
We apply the concept of castling transform of prehomogeneous vector spaces to produce new examples of minimal homogeneous Lagrangian submanifolds in the complex projective space. Furthermore we verify the Hamiltonian stability of a low…
We propose a new method for the construction of Hamiltonian-minimal and minimal Lagrangian immersions of some manifolds in $C^n$ and in $CP^n$. By this method one can construct, in particular, immersions of such manifolds as the generalized…
In this article we obtain a classification of special Lagrangian submanifolds in complex space forms subject to an $SO(2)\rtimes S_3$-symmetry on the second fundamental form. The algebraic structure of this form has been obtained by…
This is the last in a series of five papers math.DG/0211294, math.DG/0211295, math.DG/0302355, math.DG/0302356 studying compact special Lagrangian submanifolds (SL m-folds) X in (almost) Calabi-Yau m-folds M with singularities x_1,...,x_n…
We construct calibrated submanifolds of R^7 and R^8 by viewing them as total spaces of vector bundles and taking appropriate sub-bundles which are naturally defined using certain surfaces in R^4. We construct examples of associative and…
This is the first in a series of five papers math.DG/0211295, math.DG/0302355, math.DG/0302356, math.DG/0303272 studying special Lagrangian submanifolds (SL m-folds) X in (almost) Calabi-Yau m-folds M with singularities x_1,...,x_n locally…
In this short note we discuss high-dimensional examples of Legendrian submanifolds of the standard contact Euclidean space with an infinite number of exact Lagrangian fillings up to Hamiltonian isotopy. They are obtained from the examples…
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…
We present a systematic collection of results concerning interactions between convex, subharmonic and pluri-subharmonic functions on pairs of manifolds related by a Riemannian submersion. Our results are modelled on those known in the…
For a closed Riemannian manifold $M$ with a compact Lie group $G$ acting by isometries, we show that there are infinitely many $G$-invariant minimal hypersurfaces. Under the assumption that $M$ contains at most a finite number of minimal…
In this paper, we introduce the notion of a quasi-biharmonic submanifold in a pseudo-Riemannian manifold and classify quasi-biharmonic marginally trapped Lagrangian surfaces in Lorentzian complex space forms.
One generalizes the notion of Maslov class of lagrangian embeddings to symplectic vector spaces for the compact case. Topological and geometrical properties of the generalized class is discussed. Certain relationship with the minimality…
We introduce and study the notion of plurisubharmonic functions in calibrated geometry. These functions generalize the classical plurisubharmonic functions from complex geometry and enjoy their important properties. Moreover, they exist in…
A description of Lagrangian and Hamiltonian formalisms naturally arisen from the invariance structure of given nonlinear dynamical systems on the infinite--dimensional functional manifold is presented. The basic ideas used to formulate the…
Indefinite Kaehler solutions of the Einstein equations are studied, and it is almost completely determined which compact complex surfaces admit such metrics.
We classify Lagrangian submanifolds of complex space forms, whose second fundamental form can be written in a certain way, depending on a real parameter. For some special values of this parameter, the resulting submanifolds are ideal in the…
In this paper we provide an extension for the method of Discrete Lagrangian Descriptors with the purpose of exploring the phase space of unbounded maps. The key idea is to construct a working definition, that builds on the original approach…
This paper extends to dimension 4 the results in the article "Second Order Families of Special Lagrangian 3-folds" by Robert Bryant. We consider the problem of classifying the special Lagrangian 4-folds in C^4 whose fundamental cubic at…