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The axiom of cosymplectic surfaces and $W_4$-manifolds

M. B. Banaru

Smolensk State University

Abstract: An almost Hermitian manifold satisfies the cosymplectic $t$-hypersurfaces axiom, if a cosymplectic hypersurface with type number $t$ passes through every its point. It is proved that if an arbitrary $W_4$-manifold satisfies the cosymplectic $t$-hypersurfaces axiom with $t\leq1$, then this manifold is Kählerian.

Key words: almost contact metric structure, cosymplectic structure, type number, hypersurface, $W_4$-manifold.

UDC: 513.82

Received: 24.03.2014

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2015, 70:5, 213–215

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