On the Geometry of Holomorphic Developable Vector Fields on Almost Hermitian Manifolds
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The determination of conditions for the invariance of geometric objects under the action of a group of transformations is one of the most important problems of geometric research. We study the invariance conditions for almost Hermitian structures relative to the action of a local one-parameter group of diffeomorphisms generated by a developable vector field on a manifold. Moreover, we investigate the relationship between developable (in particular, concircular) vector fields on Riemannian manifolds and locally concircular transformations of the metric of these manifolds.
KeywordsRiemannian Manifold Ahlerian Manifold Hermitian Structure Riemannian Structure HERMITIAN Manifold
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