On generalized deformations of Riemannian metrics (Q2799788)

Generalized deformations of Riemannian metrics are defined as compositions of so-called rank-one deformations and conformal deformations as considered by two of the authors in [in: Trudy konferentsii ``Geometriya i prilozheniya'' posvyashchennoj 70-letiyu V. A. Toponogova, 2000. Novosibirsk: Izdatel'stvo Instituta Matematiki Im. S. L. Soboleva SO RAN. 171--182 (2001; Zbl 0990.53031)]. Here, in explicit terms, a generalized deformation \(d \bar{s}^2\) of a metric \(d s^2\) on a manifold \(M\) has the form \( d \bar{s}^2=\mu\,d s^2+\lambda\,d\theta\otimes d\theta,\) where \(\mu,\lambda,\theta\in C^\infty(M)\). Explicit expressions for the Riemannian, Ricci and Weyl curvature tensors of the deformed metrics \(d \bar{s}^2\) are obtained as well as for the scalar curvature and the Schouten tensor, called the 1-dimensional curvature here.NEWLINENEWLINEFor the entire collection see [Zbl 1298.53003].