Scalar Curvature for Middle Planes in Odd-dimensional Torse-forming Almost Ricci Solitons

Mircea Crasmareanu

We derive identities for the scalar curvature of $n$ respectively $(n+1)$-dimensional planes and their orthogonal complements in an $(2n+1)$-dimensional torse-forming almost Ricci soliton. If the torse-forming vector field is an eigenvector of the Ricci endomorphism for a special eigenvalue these identities characterize the almost Ricci soliton case.