D-homothetically fixed, weakly $(\kappa, \mu)$-structures on contact metric spaces

Philippe Rukimbira

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arXiv · 2207.06502

D-homothetically fixed, weakly $(\kappa, \mu)$-structures on contact metric spaces

Philippe Rukimbira

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Abstract

Contact metric $(\kappa ,\mu )$-spaces are generalizations of Sasakian spaces. We introduce a weak $(\kappa ,\mu )$ condition as a generalization of the K-contact one and show that many of the known results from generalized Sasakian geometry hold in the weaker generalized K-contact geometry setting. In particular, we prove existence of K-contact and $(\kappa ,\mu =2)$-structures under some conditions on the Boeckx invariant.

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BibTeX RIS

Philippe Rukimbira. 2022-07-13. D-homothetically fixed, weakly $(\kappa, \mu)$-structures on contact metric spaces. https://arxiv.org/abs/2207.06502

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