## Koji Matsumoto, Adela Mihai, and Dorotea Naitza

## Submanifolds of an even-dimensional manifold
structured by a
T-parallel connection

## (Lobachevskii Journal of Mathematics, Vol.13, pp.81-85)

Even-dimensional manifolds $N$ structured by a ${\cal T}$-parallel connection
have
been defined and studied in [DR], [MRV].
In the present paper, we assume that
$N$ carries a (1,1)-tensor field $J$ of
square $-1$ and we consider an immersion
$x:M\rightarrow N$. It is proved
that any such $M$ is a CR-product [B] and one may
decompose $M$ as $%
M=M_D\times M_{D^{\perp }}$, where $M_D$ is an invariant submanifold
of $M$
and $M_{D^{\perp }}$ is an antiinvariant submanifold of $M$.
Some other
properties regarding the immersion
$x:M\rightarrow N$ are discussed.

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