Title

Holomorphically Planar Conformal Vector Fields on almost Hermitian Manifolds

Document Type

Book Chapter

Publication Date

2003

Subject: LCSH

Geometry

Disciplines

Mathematics

Abstract

We introduce the notion of a holomorphically planar conformal vector (HPCV) field on an almost Hermitian manifold. First we generalize a result of Goldberg, showing that an HPCV on a Kaehler manifold is homothetic and analytic. Then we have proven some results on Kaehler and almost Kaehler manifolds whose curvature/Weyl conformal tensor is harmonic. In particular, we have characterized an HPCV field on the Euclidean C, S^2, C^N, and the nearly Kaehler S^6.

Comments

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Publisher Citation

Sharma, R. (2003). Holomorphically Planar Conformal Vector Fields on almost Hermitian Manifolds. Recent Advances in Riemannian and Lorentzian Geometries, 337, 145.