Warped product skew semi-invariantsubmanifolds of order $1$ of a locallyproduct Riemannian manifold

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.

Anahtar Kelimeler:

Locally product manifold, warped product submanifold, skew semi-invariant submanifold, invariant distribution, slant distribution

Warped product skew semi-invariantsubmanifolds of order $1$ of a locallyproduct Riemannian manifold

Keywords:

Locally product manifold, warped product submanifold, skew semi-invariant submanifold, invariant distribution, slant distribution,

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