Abstract
This chapter discusses the tensorial concomitants of an almost complex structure. One of the most important tensorial concomitants of an almost complex structure is the so-called Nijenhuis tensor. The chapter focuses on a real, orientable, 2n-dimensional (n > 1), ∞ differentiable manifold M2n. If x is a chart for M 2n, its associated coordinate functions will be denoted by xi, where all lower case Latin indices run from 1 to 2n and obey the summation convention. If F is any first-order tensorial concomitant of an almost complex structure, then the functions defining F can be expressed in terms of Jab and Nabc.
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