Partially Slant Submanifolds of a Kähler Manifold

Abstract

Almost Hermitian manifolds have a large number of submanifolds, such as holomorphic, totally real, CR-, slant, semi-slant, hemi-slant, bi-slant etc., depending on the behavior of the almost complex structure. In this paper, a new class of submanifolds, called partially slant submanifolds (abbreviated as PS-submanifolds), is defined, which includes the abovementioned CR-submanifolds, semi-slant submanifolds, hemi-slant submanifolds and bi-slant submanifolds. Such submanifolds of a Kaehler manifold are introduced, a proper example is given, the integrability of distributions and the geometry of maximal integral manifolds of these distributions are investigated. The effects of morphisms that naturally occur on such submanifolds on the geometry of the submanifold are investigated. In addition, special cases are determined when PS-submanifolds lie in a complex space form.