Abstract
Invariant complementary distributions are considered on para-Kenmotsu manifolds and the relations between the second fundamental form and the integrability tensor are stated. The holomorphicity of a vector field is analyzed and characterized in terms of a \(\bar{\partial }\)-operator. The connection between the Hilbert–Schmidt pseudo-norms of the two operators associated to invariant holomorphic distributions is established. Finally, applications of the Walczak formula on para-Kenmotsu manifolds are given.
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