Related papers: Sasakian Geometry: The Recent Work of Krzysztof Ga…
Wojcik's hypothesis has been mentioned on page 32 of the text S.Piekarski, "Galilean-Invariant Formulation of the Fluid Mechanics", IFTR REPORTS, 7/2007. Here we discuss it in more detail. Our main is to show that the form of the…
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The first part of these notes is a self-contained introduction to generalized complex geometry. It is intended as a `user manual' for tools used in the study of supersymmetric backgrounds of supergravity. In the second part we review some…
The purpose of this note is to introduce a new method for proving the existence of Sasakian-Einstein metrics on certain simply connected odd dimensional manifolds. We then apply this method to prove the existence of new Sasakian-Einstein…
We study the geometry of the secant and tangential variety of a cominuscule and minuscule variety, e.g. a Grassmannian or a spinor variety. Using methods inspired by statistics we provide an explicit local isomorphism with a product of an…
This is a survey article, to appear in the Proceedings of the 2018 International Congress of Mathematicians. (Revised, with added and updated references.)
The main purpose of this work is to generalize the $S^3_\bfw$ Sasaki join construction $M\star_\bfl S^3_\bfw$ described in \cite{BoTo14a} when the Sasakian structure on $M$ is regular, to the general case where the Sasakian structure is…
We study eta-Einstein geometry as a class of distinguished Riemannian metrics on contact metric manifolds. In particular, we use a previous solution of the Calabi problem for Sasakian geometry to prove the existence of eta-Einstein…
We discuss Sasakian-Einstein geometry under a quasi-regularity assumption. It is shown that the space of all quasi-regular Sasakian-Einstein orbifolds has a natural multiplication on it. Furthermore, necessary and sufficient conditions are…
Foreward to the Bolyai-Gauss-Lobachevsky 2022 special issue, published in ${\it Symmetry}$, in lieu of the 12${}^{\rm th}$ International Conference on Non-Euclidean Geometry, ``BGL-2022''.
This is a review of the main physical ideas and examples of applicability in astrophysics and pure physics of a semiclassical theory of dense matter proposed by Pavle Savic and Radivoje Kasanin in the early sixties. A hypothesis, advanced…
This article is a survey of recent results about scalar curvature and contractible open $3$-manifolds. It is dedicated to the memory of Professor S. S. Chern.
We carry on a systematic study of nearly Sasakian manifolds. We prove that any nearly Sasakian manifold admits two types of integrable distributions with totally geodesic leaves which are, respectively, Sasakian or $5$-dimensional nearly…
This review summarises the invited presentation I gave on the Milky Way disc. The idea underneath was to touch those topics that can be considered hot nowadays in the Galactic disk research: the reality of the thick disk, the spiral…
We study the critical points of monomial functions over an algebraic subset of the probability simplex. The number of critical points on the Zariski closure is a topological invariant of that embedded projective variety, known as its…
In the 1930's, Tarski introduced his plank problem at a time when the field Discrete Geometry was about to born. It is quite remarkable that Tarski's question and its variants continue to generate interest in the geometric and analytic…
One of the oldest methods for constructing integrable Hamiltonian systems, proposed by Jacobi, recently is being presented as a novel St\"{a}ckel lift construction related with Haantjes geometry. It may cause some confusion.
We prove that every nearly Sasakian manifold of dimension greater than five is Sasakian. This provides a new criterion for an almost contact metric manifold to be Sasakian. Moreover, we classify nearly cosymplectic manifolds of dimension…
With this note, we remember our friend Maria Krawczyk, who passed away this year, on May 24th. We briefly outline some of her physics interests and main accomplishments, and her great human and moral qualities.
In previous work (arXiv:2205.12067), we defined a notion of a generalized Sasakian structure in the context of generalized contact geometry, the odd dimensional analogue of generalized complex geometry introduced by Hitchin and Gualtieri.…