2023/02/06 by С. Е. Степанов, Stepanov, Sergey E., Josef Mikeš +3 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #53C20 #53C21 #53C24 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #Elasticity and Material Modeling #FOS: Mathematics #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.2302.02799
openalex publication_date 2023/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.