Related papers: Haantjes manifolds with symmetry
In this long note, we investigate various purely topological aspects of non-Hausdorff manifolds (NH-manifolds for short). Our emphasis is on manifolds which exhibit homogeneity or weakenings thereof, in particular being everywhere…
We present a theory of compatible differential constraints of a hydrodynamic hierarchy of infinite-dimensional systems. It provides a convenient point of view for studying and formulating integrability properties and it reveals some hidden…
The purpose of this paper is to give, on one hand, a mathematical exposition of the main topological and geometrical properties of geometric transitions, on the other hand, a quick outline of their principal applications, both in…
In this paper, we give the geometric meaning of hypersurfaces with constant mean curvature in a Finsler manifold by using volume preserving variation. Then we give the correspondence between principal curvatures of submanifolds by a…
The main purpose of this paper is to give a topological and symplectic classification of completely integrable Hamiltonian systems in terms of characteristic classes and other local and global invariants.
The aim of this paper is to classify compact, simply connected K\"ahler manifolds which admit totally geodesic, holomorphic complex homothetic foliation by curves.
This paper is based on the author's talk at 1997 Taniguchi Symposium ``Integrable Systems and Algebraic Geometry''. We consider an approach to the theory of Frobenius manifolds based on the geometry of flat pencils of contravariant metrics.…
In this paper we give a generalization of the normal holomorphic frames in the symplectic manifolds and find conditions for the integrability of complex structures.
In the last years many results in the area of semidefinite programming were obtained for invariant (finite dimensional, or infinite dimensional) semidefinite programs - SDPs which have symmetry. This was done for a variety of problems and…
This is the second in a series of papers. Here we develop here an intersection theory for manifolds equipped with an action of a finite group. As in our previous paper, our approach will be homotopy theoretic, enabling us to circumvent the…
Geometric Langlands duality can be understood from statements of mirror symmetry that can be formulated in purely topological terms for an oriented two-manifold $C$. But understanding these statements is extremely difficult without picking…
In this paper, we address several interconnected problems in the theory of harmonic maps between Riemannian manifolds. First, we present necessary background and establish one of the main results of the paper: a criterion characterizing…
In this lectures I explain a connection between geometric invariant theory and entanglement, and give a number of examples how this approach works.
This paper examines the broad structure on Stein manifolds and how it generalizes the notion of a domain of holomorphy in $\mathbb C^n$. Along with this generalization, we see that Stein manifolds share key properties from domains of…
An attempt is made to extend some of the basic paradigms of dynamics, from the viewpoint of (continuous) flows, to non-metric manifolds.
We present a class of thermodynamic systems with constant thermodynamic curvature which, within the context of geometric approaches of thermodynamics, can be interpreted as constant thermodynamic interaction among their components. In…
The aim of this paper is to present the first examples of compact, simply connected holomorphically pseudosymmetric Kahler manifolds.
We show that the theory of classical Hamiltonian systems admitting separating variables can be formulated in the context of ($\omega, \mathscr{H}$) structures. They are symplectic manifolds endowed with a compatible Haantjes algebra…
We study two aspects of Hecke symmetry in this note: first, we conjecture a generalization of the Ramanujan identities to the case of automorphic forms of Hecke groups; second, we conjecture a generalization of an inversion formula from the…
We prove that manifolds admitting a Riemannian metric for which products of harmonic forms are harmonic satisfy strong topological restrictions, some of which are akin to properties of flat manifolds. Others are more subtle, and are related…