ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

# Sasakian manifold

## The intrinsic geometry of almost contact metric manifolds

In this paper the notion of the intrinsic geometry of an almost contact metric manifold is introduced. Description of some classes of spaces with almost contact metric structures in terms of the intrinsic geometry is given. A new type of almost contact metric spaces, more precisely, Hermition almost contact metric spaces, is introduced.

## Refined asymptotic formulas for eigenvalues and eigenfunctions of the Dirac system with nondifferentiable potential

This paper investigates the Dirac system with the continuous potential. Asymptotic formulas for the eigenvalues (including refined) and eigenfunctions are established. As an application we obtain a theorem P. Dzhakova and B. S. Mityagin on the Riesz bases with brackets.

## Almost contact metric structures defined by connection over distribution with admissible Finslerian metric

The notion of the intrinsic connection and the extended connection of an almost contact metric manifold D with admissible Finslerian metric is introduced and studied. Using this and the extended connection on D as on the total space of a vector bundle, an almost contact metric structure is defined and investigated.