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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 7, pp. 1005–1008, July, 2013.
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Kirichenko, V.F., Kuzakon’, V.M. On the Geometry of Holomorphic Developable Vector Fields on Almost Hermitian Manifolds. Ukr Math J 65, 1122–1125 (2013). https://doi.org/10.1007/s11253-013-0846-y
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DOI: https://doi.org/10.1007/s11253-013-0846-y