FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2002, VOLUME 8, NUMBER 2, PAGES 357-364

## On the type number of nearly-cosymplectic hypersurfaces in nearly-Kählerian manifolds

M. B. Banaru

Abstract

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Nearly-cosymplectic hypersurfaces in nearly-Kählerian manifolds are considered. The following results are obtained.

Theorem 1. The type number of a nearly-cosymplectic hypersurface in a nearly-Kählerian manifold is at most one.

Theorem 2. Let s be the second fundamental form of the immersion of a nearly-cosymplectic hypersurface $\left(N,\left\{$F, x, h, g}) in a nearly-Kählerian manifold $M2n$. Then $N$ is a minimal submanifold of $M2n$ if and only if s (x, x) = 0.

Theorem 3. Let $N$ be a nearly-cosymplectic hypersurface in a nearly-Kählerian manifold $M2n$, and let $T$ be its type number. Then the following statements are equivalent:

1) $N$ is a minimal submanifold of $M2n$;

2) $N$ is a totally geodesic submanifold of $M2n$;

3) $T$º 0.

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