FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2000, VOLUME 6, NUMBER 4, PAGES 1095-1120

V. F. Kirichenko

Abstract

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We study the differential geometry of principal toroidal fiber bundles
of arbitrary rank over a smooth manifold that may be equipped with some
additional structure. The explicit calculation is given for
the characteristic class of the canonical principal
```$T^1$ -bundle over
an almost Hermitian manifold. We study the structure of
Riemann--Christoffel tensor and Ricci tensor of the canonical
pseudo-Riemannian structure induced on the space of the principal
toroidal fiber bundle over a pseudo-Riemannian manifold, and a criterion
is found for this structure to be Einstein one. We study the properties
of the almost contact metric structure canonically induced on the space
of a canonical principal toroidal fiber bundle over an almost Hermitian
manifold. The obtained results generalize some known results in this area
and allow to build new interesting examples of almost contact metric
structures of various classes.

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