Kenmotsu manifold


In the mathematical field of differential geometry, a Kenmotsu manifold is an almost-contact manifold endowed with a certain kind of Riemannian metric.


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


  • David E. Blair. Riemannian geometry of contact and symplectic manifolds. Second edition. Progress in Mathematics, 203. Birkhäuser Boston, Ltd., Boston, MA, 2010. ISBN 978-0-8176-4958-6, doi:10.1007/978-0-8176-4959-3 closed access
  • Katsuei Kenmotsu. A class of almost contact Riemannian manifolds. Tohoku Mathematical Journal (2) 24 (1972), 93–103. doi:10.2748/tmj/1178241594 icon of an open green padlock