Geometry of Kenmotsu manifolds.

*(English)*Zbl 1129.53001
Braşov: Publishing House of Transilvania University of Braşov (ISBN 978-973-635-952-1/pbk). iv, 160 p. (2007).

Contact geometry turns out to be an important branch in differential geometry with many applications in mathematical physics. Kenmotsu manifolds appeared in 1972 and acquired relevance in the last 25 years. They constitue a valuable chapter in contact geometry and they are in some sense, complementary to Sasaki manifolds.

The aim of the author is to present an updated state concerning Kenmotsu manifolds, beginning with an introduction to contact structures. Next, the author presents general properties of Kenmotsu manifolds and contact submersions. After this the author studies curvature problems and finally he goes to more specific properties and types of Kenmotsu structures. The book gives a idea of the principal questions concerning this matter, with a clear presentation of the difficulties. It is a good introduction to the field and it promotes to try with the topic since there are many open problems to be attacked. The aim of the book is achieved.

The aim of the author is to present an updated state concerning Kenmotsu manifolds, beginning with an introduction to contact structures. Next, the author presents general properties of Kenmotsu manifolds and contact submersions. After this the author studies curvature problems and finally he goes to more specific properties and types of Kenmotsu structures. The book gives a idea of the principal questions concerning this matter, with a clear presentation of the difficulties. It is a good introduction to the field and it promotes to try with the topic since there are many open problems to be attacked. The aim of the book is achieved.

Reviewer: Gabriela P. Ovando (Santa Fé)