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Kenmotsu manifold

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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

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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.[1]

An almost-contact metric manifold is said to be a Kenmotsu manifold if[2]

References

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  1. ^ Blair 2010, p. 44.
  2. ^ Blair 2010, p. 98.

Sources

  • Blair, David E. (2010). Riemannian geometry of contact and symplectic manifolds. Progress in Mathematics. Vol. 203 (Second edition of 2002 original ed.). Boston, MA: Birkhäuser Boston, Ltd. doi:10.1007/978-0-8176-4959-3. ISBN 978-0-8176-4958-6. MR 2682326. Zbl 1246.53001.
  • Kenmotsu, Katsuei (1972). "A class of almost contact Riemannian manifolds". Tohoku Mathematical Journal. Second Series. 24 (1): 93–103. doi:10.2748/tmj/1178241594. MR 0319102. Zbl 0245.53040.