arXiv subjects

Aleksandra Fedorova

Publications and source records attributed to Aleksandra Fedorova.

2 recordsLinked to original sources

arXiv2012

Degree of mobility for metrics of lorentzian signature and parallel (0,2)-tensor fields on cone manifolds

Degree of mobility of a (pseudo-Riemannian) metric is the dimension of the space of metrics geodesically equivalent to it. We describe all possible values of the degree of mobility on a simply connected n-dimensional manifold of lorentz signature. As an application we calculate all possible differences between the dimension of the projective and the isometry groups. One of the main new technical results in the proof is the description of all parallel symmetric (0,2)-tensor fields on cone manifolds of signature $(n-1,2).

math.DG↗

arXiv2010

The Tanno-Theorem for Kählerian metrics with arbitrary signature

Considering a non-constant smooth solution $f$ of the Tanno equation on a closed, connected Kähler manifold $(M,g,J)$ with positively definite metric $g$, Tanno showed that the manifold can be finitely covered by $(\mathbb{C}P(n),\mbox{const}\cdot g_{FS})$, where $g_{FS}$ denotes the Fubini-Study metric of constant holomorphic sectional curvature equal to $1$. The goal of this paper is to give a proof of Tannos Theorem for Kähler metrics with arbitrary signature.

math.DG↗