FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2002, VOLUME 8, NUMBER 2, PAGES 357-364
M. B. Banaru
Abstract
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Nearly-cosymplectic hypersurfaces in nearly-K\"ahlerian manifolds
are considered. The following results are obtained.
\textbf{Theorem 1.}
The type number of a nearly-cosymplectic hypersurface
in a nearly-K\"ahlerian manifold is at most one.
\textbf{Theorem 2.}
Let $\sigma$ be the second fundamental form of the immersion of
a nearly-cosymplectic hypersurface $(N,\{\Phi,\xi,\eta,g\})$
in a nearly-K\"ahlerian manifold $M^{2n}$ . Then $N$ is a minimal
submanifold of $M^{2n}$ if and only if $\sigma(\xi,\xi) = 0$ .
\textbf{Theorem 3.}
Let $N$ be a nearly-cosymplectic hypersurface
in a nearly-K\"ahlerian manifold $M^{2n}$ , and let $T$
be its type number. Then the following statements are equivalent:
1) $N$ is a minimal submanifold of $M^{2n}$ ;
2) $N$ is a totally geodesic submanifold of $M^{2n}$ ;
3) $T \equiv 0$ .
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Last modified: November 26, 2002