In the mathematical field of differential geometry, a Kenmotsu manifold is an almost-contact manifold endowed with a certain kind of Riemannian metric. They are named after the Japanese mathematician Katsuei Kenmotsu.
Definitions Let be an almost-contact manifold. One says that a Riemannian metric on is adapted to the almost-contact structure if:
That is to say that, relative to the vector has length one and is orthogonal to furthermore the restriction of to is a Hermitian metric relative to the almost-complex structure One says that is an almost-contact metric manifold.
An almost-contact metric manifold is said to be a Kenmotsu manifold if
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