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 $$s be the second
fundamental form of the immersion of a nearly-cosymplectic
hypersurface $(N,\{$F, x,
h, g}) in
a nearly-Kählerian manifold $M2n$.
Then $N$ is
a minimal submanifold of $M2n$ if and only
if $$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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Location: http://mech.math.msu.su/~fpm/eng/k02/k022/k02203h.htm

Last modified: November 26, 2002