https://neckpinch.com/authors/irina-tsyganok/New arXiv papers by Irina Tsyganok, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2608.08233arxiv:2608.08233Sat, 08 Aug 2026 00:00:00 GMTSergey Stepanov, Irina Tsyganok — Let (M,g) be a compact n-dimensional Riemannian manifold, n>2. We introduce a restricted variational principle for the Einstein-Hilbert functional by requiring the admissible metric variations to satisfy the harmonic gauge condition. We derive the corresponding Euler-Lagrange equation and show that a metric is critical with respect to all volume-preserving harmonic variations if and only if its Einstein tensor differs from a multiple of the metric by an element of the image of the adjoint Bianchi operator. We prove that every harmonic critical metric determines a compact Ricci soliton whose soliton constant is given by the normalized Einstein-Hilbert functional. By Perelman's theorem, every such metric is in fact the metric of a compact gradient Ricci soliton. Conversely, every compact gradient Ricci soliton satisfies the restricted Euler-Lagrange equation. Thus, a compact Riemannian metric is harmonic critical if and only if it is the metric of a compact gradient Ricci soliton. We further show that the gauge one-form differs from the negative differential of a soliton potential by a Killing one-form. In particular, if the Ricci tensor is negative definite, then the gauge one-form vanishes and the metric is Einstein. Moreover, every non-Einstein harmonic critical metric is necessarily shrinking.Ricci solitons https://arxiv.org/abs/2304.03584arxiv:2304.03584Fri, 07 Apr 2023 00:00:00 GMTVladimir Rovenski, Sergey Stepanov, Irina Tsyganok — In the paper, we study complete almost Ricci solitons using the concepts and methods of geometric dynamics and geometric analysis. In particular, we characterize Einstein manifolds in the class of complete almost Ricci solitons. Then, we examine compact almost Ricci solitons using the orthogonal expansion of the Ricci tensor, this allows us to substantiate the concept of almost Ricci solitons.Ricci solitonsEinstein metricsAlmost & η-Ricci solitons https://arxiv.org/abs/2302.02799arxiv:2302.02799Mon, 06 Feb 2023 00:00:00 GMTSergey E. Stepanov, Josef Mikes, Irina I. Tsyganok — In this article, we consider an orthogonal decomposition of the traceless part of the Ricci tensor of a compact Riemannian manifold and study its application to the geometry of compact almost Ricci solitons. In addition, we consider an orthogonal expansion of the traceless part of the second fundamental form of a compact spacelike hypersurface in a Lorentzian manifold and study its application to the problem of constructing solutions of general relativistic constraint equations in vacuum. In these two cases, we use the well-known Ahlfors Laplacian.Ricci solitonsAlmost & η-Ricci solitonsPhysics