Abstract
We study a nearly Kaehler manifold M admitting a closed conformal vector field V, and obtain three results under the following assumptions (i) V is almost analytic, (ii) M has real dimension \(>6\), is complete and strictly nearly Kaehler, and (iii) M is complete strictly nearly Kaehler of global constant type.
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References
Bochner, S.: Curvature and Betti numbers. II. Ann. Math. 50, 77–93 (1949)
Chen, B.: Pseudo-Riemannian Geometry,\(\delta \)-Invariants and Applications. World Scientific, Singapore (2011)
Deshmukh, S.: Conformal vector fields on Kaehler manifolds. Ann. Dell ’Univ. ’Di Ferrara 57, 17–26 (2011)
Ejiri, N.: Totally real submanifolds in a 6-sphere. Proc. Am. Math. Soc. 83, 759–763 (1981)
Euh, Y., Sekigawa, K.: Notes on strictly nearly Kaehler Einstein manifolds. Comptes Rendus Acad. Bulgare Sci. 64, 791–798 (2011)
Goldberg, S.I.: Curvature and Homology. Academic Press, New York (1964)
Gray, A.: Almost complex submanifolds of the six-sphere. Proc. Am. Math. Soc. 20, 277–279 (1969)
Gray, A.: Nearly Kähler manifolds. J. Differ. Geom. 4, 283–309 (1970)
Gray, A.: The structure of nearly Kähler manifolds. Math. Ann. 223, 233–248 (1976)
Gray, A., Hervella, L.: The sixteen classes of almost Hermitian manifolds and their linear invariants. Ann. Mat. Pura Ed Appl. 123, 35–58 (1980)
Nagy, P.: On nearly-Kähler geometry. Ann. Glob. Anal. Geom. 22, 167–178 (2002)
Naveira, A.M., Semmelmann, U.: Conformal Killing forms on nearly Kaehler manifolds. Differ. Geom. Appl. 70, 101620–101629 (2020)
Obata, M.: Riemannian manifolds admitting a solution of a certain system of differential equations. In: Differential Geometry. Kyoto, Proc. US-Japan Sem, pp. 101–114 (1965)
Ros, A., Urbano, F.: Lagrangian submanifolds of Cn with conformal Maslov form and the Whitney sphere. J. Math. Soc. Jpn. 50, 203–226 (1998)
Tanno, S., Weber, W.: Closed conformal vector fields. J. Differ. Geom. 3, 361–366 (1969)
Tashiro, Y.: Complete Riemannian manifolds and some vector fields. Trans. Am. Math. Soc. 117, 251–275 (1965)
Yano, K.: Differential Geometry on Complex and Almost Complex Spaces. Pergamon Press, New York (1965)
Acknowledgements
Rahul Poddar was funded by the University Grants Commission (UGC), India, in the form of Senior Research Fellowship.
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Poddar, R., Balasubramanian, S. & Sharma, R. Nearly Kaehler manifolds admitting a closed conformal vector field. Beitr Algebra Geom 65, 209–216 (2024). https://doi.org/10.1007/s13366-023-00682-2
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DOI: https://doi.org/10.1007/s13366-023-00682-2