Let be a locally product Riemannian manifold, where is a Riemannian metric and is a non-trivial tensor field of type (1,1) satisfying the following conditions:
being the Levi-Civita connection on .
The authors study slant, bi-slant and semi-slant submanifolds of a locally product manifold.
Let be a Riemannian manifold which is isometrically immersed in a locally product manifold . For each nonzero vector tangent to at , denotes the angle between and . is said to be slant if the angle is a constant, independent of the choice of and . The authors give useful characterizations of slant submanifolds in a locally product manifold.
Next the authors consider bi-slant submanifolds and, finally, semi-slant submanifolds. is called a semi-slant submanifold of if there exist two orthogonal distributions and on such that , the distribution is invariant, i.e., and the distribution is slant. The authors give necessary and sufficient condition for a submanifold of a locally product manifold to be semi-slant. They also obtain integrability conditions for the distributions and mentioned above.