6 citations · 15 across the 6 of their papers we have counts for
6 papers
Conformal geodesics are not variational in higher dimensions
Boris Kruglikov
Variationality of the equation of conformal geodesics is an important problem in geometry with applications to general relativity. Recently it was proven that, in three dimensions,…
Involutive scroll structures on solutions of 4D dispersionless integrable hierarchies
Evgeny Ferapontov, Boris Kruglikov
A rational normal scroll structure on an -dimensional manifold is defined as a field of rational normal scrolls of degree in the projectivised cotangent bundle $\m…
Second-order PDEs in 4D with half-flat conformal structure
Sobhi Berjawi, Eugene Ferapontov, Boris Kruglikov +1
We study second-order PDEs in 4D for which the conformal structure defined by the characteristic variety of the equation is half-flat (self-dual or anti-self-dual) on every solutio…
Integrability of dispersionless Hirota type equations in 4D and the symplectic Monge-Ampere property
E. V. Ferapontov, B. Kruglikov, V. Novikov
We prove that integrability of a dispersionless Hirota type equation implies the symplectic Monge-Ampere property in any dimension . In 4D this yields a complete classifica…
Compatibility of Gauss maps with metrics
J. Eschenburg, B. S. Kruglikov, V. S. Matveev +1
We give necessary and sufficient conditions on a smooth local map of a Riemannian manifold into the sphere to be the Gauss map of an isometric immersion …
Deformation of big pseudoholomorphic disks and application to the Hanh pseudonorm
B. Kruglikov
We simplify proof of the theorem that close to any pseudoholomorphic disk there passes a pseudoholomorphic disk of arbitrary close size with any pre-described sufficiently close di…