On the sectional curvature of Kahler manifolds of indefinite metrics
Some curvature properties of Kahler manifolds of indefinite metrics are studied. Analogues of a Kulkarni's theorem are proved for such manifolds.
math.DG↗
arXiv subjects
Adrijan Borisov
Publications and source records attributed to Adrijan Borisov.
Curvature properties and isotropic planes of Riemannian and almost Hermitian manifolds of indefinite metrics
We study two types of isotropic planes: weakly isotropic and strongly isotropic planes. We prove that a Riemannian manifold of indefinite metric is conformally flat if and only if its curvature tensor vanishes on all the strongly isotropic planes. We specialize the plane axiom for Riemannian manifolds of indefinite metrics. We show that manifolds satisfying plane axiom of weakly (strongly) isotropic planes are of constant sectional curvature (conformaly flat). Further we study analogous problems on almost Hermitian manifolds of indefinite metrics.
math.DG↗
On the boundedness of the sectional curvature of almost Hermitian manifolds
We prove the following results: An almost Hermitian manifold of indefinite metric is of pointwise constant holomorphic sectional curvature if the holomorphic sectional curvature is bounded from above and from below. If the antiholomorphic sectional curvature is bounded either from above or from below, then the manifold is of pointwise constant antiholomorphic sectional curvature. Similar results are obtained for almost Hermitian manifolds of definite metric.
math.DG↗