Professor KIRILL KRASNOV's Outputs (4)

Dynamics of Cayley forms (2025)
Journal Article
Krasnov, K. (2025). Dynamics of Cayley forms. Pure and Applied Mathematics Quarterly, 21(5), 1959-2003. https://doi.org/10.4310/pamq.250421122254

The most natural first-order PDE's to be imposed on a Cayley 4-form in eight dimensions is the condition that it is closed. As is well-known, this implies integrability of the Spin(7)-structure defined by the Cayley form, as well as Ricci-flatness of th... Read More about Dynamics of Cayley forms.

Spinors from pure spinors (2025)
Journal Article
Bhoja, N., & Krasnov, K. (in press). Spinors from pure spinors. Quarterly Journal of Mathematics,

We propose and develop a new method to classify orbits of the spin group Spin(2d) in the space of its semi-spinors. The idea is to consider spinors as being built as a linear combination of their pure constituents. As is well-known, two pure spinors... Read More about Spinors from pure spinors.

Pure connection formalism and Plebanski’s second heavenly equation (2025)
Journal Article
Krasnov, K., & Lipstein, A. (2025). Pure connection formalism and Plebanski’s second heavenly equation. Journal of High Energy Physics, 2025(3), Article 152. https://doi.org/10.1007/jhep03%282025%29152

Plebanski’s second heavenly equation reduces the problem of finding a self-dual Einstein metric to solving a non-linear second-order PDE for a single function. Plebanski’s original equation is for self-dual metrics obtained as perturbations of the fl... Read More about Pure connection formalism and Plebanski’s second heavenly equation.

Kerr metric from two commuting complex structures (2025)
Journal Article
Krasnov, K., & Shaw, A. (2025). Kerr metric from two commuting complex structures. Classical and Quantum Gravity, 42(6), Article 065013. https://doi.org/10.1088/1361-6382/adb531

The main aim of this paper is to simplify and popularise the construction from the 2013 paper by Apostolov, Calderbank, and Gauduchon, which (among other things) derives the Pleba´nskiPleba´nski-Demia´nskiDemia´nski family of solutions of GR using id... Read More about Kerr metric from two commuting complex structures.