Abstract
We determine Kenmotsu spaces which are also either D’Atry spaces (that is, all of whose local geodesic symmetries are volume-preserving) or C-spaces (that is, their Jacobi operators have constant eigenvalues along the corresponding geodesics). We prove that both D’Atry and C-type Kenmotsu spaces are of constant sectional curvature-1.
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The authors want to thank the referee of this paper for his/her really valuable comments, which helped to improve the original manuscript.
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Alfonso Carriazo is partially supported by the MINECO-FEDER Grant MTM2014-52197-P. He is a member of the IMUS (Instituto de Matemáticas de la Universidad de Sevilla), and of the PAIDI group FQM-327 (Junta de Andalucía, Spain). Jong Taek Cho was supported in part by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2016R1D1A1B03930756).
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Carriazo, A., Cho, J.T. D’Atri and C-Type Kenmotsu Spaces. Results Math 73, 45 (2018). https://doi.org/10.1007/s00025-018-0780-2
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DOI: https://doi.org/10.1007/s00025-018-0780-2