HyperKahler contact Distribution in 3-Sasakain Manifolds

Abstract

In this paper, the HyperKahler contact distribution of a 3-Sasakian manifold is studied. To analyze the curvature properties of this distribution, the special metric connection $\bar{\nabla }$ is defined. This metric connection is completely determined by HyperKahler contact distribution. We prove that HyperKahler contact distribution is of constant holomorphic sectional curvatures if and only if its 3-Sasakian manifold is of constant ${\phi }_{\alpha }$-sectional curvatures. Moreover, it is shown that there is an interesting relation between the sectional curvatures of ${\phi }_{\alpha }$-planes on $TM$ of metric connection $\bar{\nabla }$ and the Levi-Civita connection.

A new version with major changes is available now

References in corpus (1)

• 3-Sasakian manifolds, 3-cosymplectic manifolds and Darboux theorem