Holomorphic harmonic morphisms from cosymplectic almost Hermitian manifolds

We study 4-dimensional orientable Riemannian manifolds equipped with a minimal and conformal foliation F of codimension 2. We prove that the two adapted almost Hermitian structures J 1 and J 2 are both cosymplectic if and only if F is Riemannian and its horizontal distribution H is integrable.

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Bibliographic Details
Published in:	Geometriae dedicata Vol. 178; no. 1; pp. 143 - 150
Main Author:	Gudmundsson, Sigmundur
Format:	Journal Article
Language:	English
Published:	Dordrecht Springer Netherlands 01-10-2015
Subjects:	Algebraic Geometry Convex and Discrete Geometry cosymplectic Differential Geometry Geometri Geometry harmonic morphisms holomorphic Hyperbolic Geometry Matematik Mathematics Mathematics and Statistics Natural Sciences Naturvetenskap Original Paper Projective Geometry Topology Cosymplectic Harmonic morphisms 58E20 53C12 53C43 Holomorphic
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Description
Summary:	We study 4-dimensional orientable Riemannian manifolds equipped with a minimal and conformal foliation F of codimension 2. We prove that the two adapted almost Hermitian structures J 1 and J 2 are both cosymplectic if and only if F is Riemannian and its horizontal distribution H is integrable.
ISSN:	0046-5755 1572-9168
DOI:	10.1007/s10711-015-0049-9