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.
This is a preview of subscription content, log in via an institution to check access.
References
A.V. Aminova, Projective Transformations of Pseudo-Riemannian Manifolds [in Russian], Yanus-K, Moscow (2003).
E. Kaehler, “Uber eine bemerkenswerte Hermitische Metrik,” Abh. Math. Sem. Hamburgischen Univ., 9, 173–186 (1933).
K. Yano, “Concircular geometry. I–4,” Proc. Imp. Acad. Jpn., 16, 195–200, 354–360, 442–448, 505–511 (1940).
Author information
Authors and Affiliations
Additional information
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 7, pp. 1005–1008, July, 2013.
Rights and permissions
About this article
Cite this article
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
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-013-0846-y