We introduce warped product skew semi-invariant submanifolds of order $1$ of a locally product Riemannian manifold. We give a necessary and sufficient condition for a skew semi-invariant submanifold of order 1 to be a locally warped product. We also establish an inequality between the warping function and the squared norm of the second fundamental form for such submanifolds. The equality case is also discussed.
Locally product manifold, warped product submanifold, skew semi-invariant submanifold, invariant distribution, slant distribution
TAŞTAN, HAKAN METE
"Warped product skew semi-invariantsubmanifolds of order $1$ of a locallyproduct Riemannian manifold,"
Turkish Journal of Mathematics: Vol. 39:
4, Article 1.
Available at: https://journals.tubitak.gov.tr/math/vol39/iss4/1