Related papers: A Note on Twistor Integrals
In this survey, we describe the fundamental differential-geometric structures of information manifolds, state the fundamental theorem of information geometry, and illustrate some use cases of these information manifolds in information…
This note is the sequel of "Geometric structures as variational objects, I." It generalizes the main result and perspectives of that work to a class of geometric structures that includes integrable almost-complex structures.
This note provides a variational description of the most basic differential geometric structures on a smooth manifold.
We first make a little survey of the twistor theory for hypercomplex, generalized hypercomplex, quaternionic or generalized quaternionic manifolds. This last theory was iniated by Pantilie, who shows that any generalized almost quaternionic…
A twistorial formulation of a particle of arbitrary spin has been constructed. Equations of the twistor formulation are obtained for massive and massless spinning particles. The twistor space of the massive particle is formed by two…
In this document we present a twistor correspondence for half-flat almost-Grassmannian structures on real and complex manifolds. We provide foundational results regarding local theory in the complex setting and a global correspondence when…
This book is a textbook for the course of foundations of geometry. It is addressed to mathematics students in Universities and to High School students for deeper learning the elementary geometry. It can also be used in mathematics coteries…
These notes present elementary introduction to tractors based on classical examples, together with glimpses towards modern invariant differential calculus related to vast class of Cartan geometries, the so called parabolic geometries.
We present a generalization of the spinor and twistor geometry for on (pseudo) Riemannian manifolds enabled with nonholonomic distributions or for Finsler-Cartan spaces modelled on tangent Lorentz bundles. Nonholonomic (Finsler) twistors…
It is well known that twistor constructions can be used to analyse and to obtain solutions to a wide class of integrable systems. In this article we express the standard twistor constructions in terms of the concept of an admissible family…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
This is a brief introduction to the basic concepts of topology. It includes the basic constructions, discusses separation properties, metric and pseudometric spaces, and gives some applications arising from the use of topology in computing.
This paper introduces the notion of twisted toric manifolds which is a generalization of one of symplectic toric manifolds, and proves the weak Delzant type classification theorem for them. The computation methods for their fundamental…
Survey article on the geometry of spherical varieties. Invited survey for Transformation Groups.
This article describes some aspects of Cauchy integrals and related geometry of sets and measures in Euclidean spaces, etc.
This primer is intended as an introduction to differential forms, a central object in modern mathematical physics, for scientists and engineers.
This is an introduction to the algebraic aspect of Teichm\"uller dynamics, with a focus on its interplay with the geometry of moduli spaces of curves as well as recent advances in the field.
Twistor methods provide a powerful tool in the study of harmonic maps and harmonic morphisms. Indeed, their use has enabled us to produce a variety of examples of harmonic morphisms defined on 4-dimensional manifolds, and a complete…
A survey on recent developments in (algebraic) integral geometry is given. The main focus lies on algebraic structures on the space of translation invariant valuations and applications in integral geometry.
These are course notes I wrote for my Fall 2013 graduate topics course on geometric structures, taught at ICERM. The notes rework many of proofs in William P. Thurston's beautiful but hard-to-understand paper, "Shapes of Polyhedra". A…