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

View as HTML     View as gif image    View as LaTeX source

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.

All articles are published in Russian.

Location: http://mech.math.msu.su/~fpm/eng/k02/k022/k02203h.htm
Last modified: November 26, 2002