Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10734775 | Journal of Geometry and Physics | 2005 | 15 Pages |
Abstract
Using the one-to-one correspondence between Kähler-Norden and holomorphic Riemannian metrics, important relations between various Riemannian invariants of manifolds endowed with such metrics are established. Especially, the holomorphic versions of the recurrence of the Riemann, Ricci, projective are defined and investigated. For four-dimensional Kähler-Norden manifolds, it is proved that they are of holomorphically recurrent curvature on the set where the holomorphic scalar curvature does not vanish. Furthermore, a four-dimensional Kähler-Norden manifold is (locally) conformally flat if and only if its holomorphic scalar curvature is constant pure imaginary. The present paper continues author's investigations of Kähler-Norden manifolds from the papers [K. SÅuka, On Kähler manifolds with Norden metrics, An. Åtiint. Univ. Al.I. Cuza IaÅI Ser. Ia Mat. 47 (2001) 105-122; K. SÅuka, Properties of the Weyl conformal curvature of Kähler-Norden manifolds, in: Proc. Colloq. Diff. Geom. on Steps in Differential Geometry, July 25-30, 2000, Debrecen, 2001, pp. 317-328].
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Karina SÅuka,