ALMOST CONTACT METRIC STRUCTURES DEFINED BY AN $N$-PROLONGED CONNECTION
The notion of intrisic and N-extended connections are introduced on a manifold with an almost contact metric structure $(\varphi,\overrightarrow{\xi},\eta,g,X,D)$. Using $N$-extended connection, we define a new almost contact metric structure on the distribution $D$, which is called an extended almost contact metric structure. We study properties of this structure.