FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2010, VOLUME 16, NUMBER 1, PAGES 81-93

$r$-tuple almost product structures

A. G. Kushner

Abstract

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A generalization of an almost product structure and an almost complex structure on smooth manifolds is constructed. The set of tensor differential invariants of type $(2,1)$ and the set of the differential $2$-forms for such structures are constructed. We show how these tensor invariants can be used to solve the classification problem for Monge--Ampère equations and Jacobi equations.

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Last modified: March 11, 2011