CR-warped product submanifolds of locally conformal Kaehler manifolds

In the present paper characterizations in terms of the canonical structures P and F on a CR-submanifold of a locally conformal Kaehler manifold are worked out under which the sub manifold reduces to a CR-warped product submanifold

Warped Product Semi-Slant Submanifolds of a Sasakian Manifold

2000 Mathematics Subject Classification: 53C40, 53C25.In the present note, it is proved that there donot exist warped product semi-slant submanifolds in a Sasakian manifold other than contact CR-warped product submanifolds and thus the results obtained in [8] are generalized

Classification of totally umbilical ξ⊥\xi^\perp CR-submanifolds of cosymplectic manifolds

In [6], Cabras, Ianus and Pitis proved that in a cosymplectic manifold there does not exist any extrinsic sphere tangent to the structure vector field xi. We consider the structure vector field xi normal to the submanifold in the sense of Papaghiuc [12] and derive that a totally umbilical CR-submanifold of a cosymplectic manifold is either (i) totally geodesic, (ii) anti-invariant or (iii) an extrinsic spher

CLASSIFICATION OF TOTALLY UMBILICAL xi(perpendicular to) CR-SUBMANIFOLDS OF COSYMPLECTIC MANIFOLDS

In [6], Cabras, Ianus and Pitis proved that in a cosymplectic manifold there does not exist any extrinsic sphere tangent to the structure vector field xi. We consider the structure vector field xi normal to the submanifold in the sense of Papaghiuc [12] and derive that a totally umbilical CR-submanifold of a cosymplectic manifold is either (i) totally geodesic, (ii) anti-invariant or (iii) an extrinsic spher

A Classification of a Totally Umbilical Slant Submanifold of Cosymplectic Manifolds

We study slant submanifolds of a cosymplectic manifold. It is shown that a totally umbilical slant submanifold of a cosymplectic manifold is either an anti-invariant submanifold or a 1−dimensional submanifold. We show that every totally umbilical proper slant submanifold of a cosymplectic manifold is totally geodesic

A classification of totally umbilical slant submanifolds of cosymplectic manifolds

We study slant submanifolds of a cosymplectic manifold. It is shown that a totally umbilical slant submanifold M of a cosymplectic manifold M is either an anti-invariant submanifold or a 1−dimensional submanifold. We show that every totally umbilical proper slant submanifold of a cosymplectic manifold is totally geodesic