FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

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

**Differential geometry of principal toroidal fiber bundles**

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 $T1$-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.

All articles are
published in Russian.

Location: http://mech.math.msu.su/~fpm/eng/k00/k004/k00410h.htm

Last modified: February 13, 2001