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On almost hyperHermitian structures on Riemannian manifolds and tangent bundles

Serge Bogdanovich, Alexander Ermolitski (2004)

Open Mathematics

Some results concerning almost hyperHermitian structures are considered, using the notions of the canonical connection and the second fundamental tensor field h of a structure on a Riemannian manifold which were introduced by the second author. With the help of any metric connection $\tilde{\nabla}$ on an almost Hermitian manifold M an almost hyperHermitian structure can be constructed in the defined way on the tangent bundle TM. A similar construction was considered in [6], [7]. This structure includes two basic...

On holomorphically projective mappings from manifolds with equiaffine connection onto Kähler manifolds

Irena Hinterleitner, Josef Mikeš (2013)

Archivum Mathematicum

In this paper we study fundamental equations of holomorphically projective mappings from manifolds with equiaffine connection onto (pseudo-) Kähler manifolds with respect to the smoothness class of connection and metrics. We show that holomorphically projective mappings preserve the smoothness class of connections and metrics.

On holomorphically projective mappings of $e$ -Kähler manifolds

Irena Hinterleitner (2012)

Archivum Mathematicum

In this paper we study fundamental equations of holomorphically projective mappings of $e$ -Kähler spaces (i.e. classical, pseudo- and hyperbolic Kähler spaces) with respect to the smoothness class of metrics. We show that holomorphically projective mappings preserve the smoothness class of metrics.

On representation theory and the cohomology rings of irreducible compact hyperkähler manifolds of complex dimension four

Daniel Guan (2003)

Open Mathematics

In this paper, we continue the study of the possible cohomology rings of compact complex four dimensional irreducible hyperkähler manifolds. In particular, we prove that in the case b 2=7, b 3=0 or 8. The latter was achieved by the Beauville construction.

On the asymptotic geometry of gravitational instantons

Vincent Minerbe (2010)

Annales scientifiques de l'École Normale Supérieure

We investigate the geometry at infinity of the so-called “gravitational instantons”, i.e. asymptotically flat hyperkähler four-manifolds, in relation with their volume growth. In particular, we prove that gravitational instantons with cubic volume growth are ALF, namely asymptotic to a circle fibration over a Euclidean three-space, with fibers of asymptotically constant length.