Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 5 (2010), 201 -- 213


Novac-Claudiu Chiriac

Abstract. We introduce (g,F)-manifolds and initiate a study of their semi-invariant submanifolds. These submanifolds are generalizations of CR-submanifolds of Kaehler manifolds. We obtain necessary and sufficient conditions for the integrability of distributions on a semi-invariant submanifold and study the geometry of foliations defined by these distributions. In particular, for a large class of (g,F)-manifolds we prove the existence of a natural foliation on their semi-invariant submanifolds.

2010 Mathematics Subject Classification: 53C40, 53C15.
Keywords: semi-invariant submanifold; (g,F)-manifold; Distribution; Foliation.

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\noindent Novac-Claudiu Chiriac
University Constantin Brâncuşi of Târgu-Jiu
Str. Geneva, Nr. 3, 210136 Târgu-Jiu, Romania.