Riemannian manifolds with a parallel field of complex planes |
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Authors: | Izu Vaisman |
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Affiliation: | (1) Department of Mathematics, University of Haifa, Israel |
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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, 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 thempartially 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.To Prof. R. Artzy on his 70th Birthday |
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