On two structural tensors of an acm-structure

Abstract

Almost contact metric structures on odd-dimensional manifolds are considered. The first group of the Cartan structural equations of an arbi­trary almost contact metric structure written in an A-frame (i. e., in a fra­me adapted to this almost contact metric structure) is studied. It is proved that the fifth and sixth Kirichenko structural tensors of the almost contact metric structure vanish if and only if the structural contact form is closed.

Keywords

• almost contact metric structure
• cartan structural equa­tions
• structural tensors
• contact form
• kirichenko — uskorev structure