## Abstract

The purpose of this paper is to discuss Riemannian manifolds which admit a parallel field of complex planes, consisting of vectors of the form {Mathematical expression}, where a,b are real orthogonal vectors of equal length. Using the Nirenberg Frobenius Theorem [12], it follows that these are reducible Riemannian manifolds, whose metric is locally a sum of a Kähler and of a Riemann metric, and we are calling them partially Kähler manifolds. After a general presentation of these manifolds (including a general presentation of the complex integrable plane fields) we are discussing harmonic forms, Betti numbers, and Dolbeault cohomology. This discussion is based on a theorem of Chern [4], and it provides generalizations of the results of Goldberg [9], as well as some other new results.

Original language | English |
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Pages (from-to) | 174-192 |

Number of pages | 19 |

Journal | Journal of Geometry |

Volume | 17 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1981 |

## ASJC Scopus subject areas

- Geometry and Topology