Canonical Submersions in Nearly Kähler Geometry

Abstract

We explore submersions introduced by reducible holonomy representations of connections with parallel skew torsion. A submersion theorem extending previous, less general, results is given. As our main application we show that parallel 3-$(\alpha ,\delta )$-Sasaki manifolds admit 1-dimensional submersions onto nearly Kähler orbifolds. As a secondary application we reprove that a certain class of nearly Kähler manifolds submerges onto quaternionic Kähler manifolds. This new proof gives an direct expression for the quaternionic structure on the base.

arXiv comment14 pages, published version

References in corpus (5)

• Superstrings with Intrinsic Torsion
• Metric connections with parallel skew-symmetric torsion
• Generalizations of 3-Sasakian manifolds and skew torsion
• Spin(9)-structures and connections with totally skew-symmetric torsion
• Homogeneous non-degenerate $3$-$(\alpha ,\delta )$-Sasaki manifolds and submersions over quaternionic Kähler spaces