Pointwise Semi-Slant Submersions Whose Total Manifolds Are Locally Product Riemannian Manifolds
In this paper, we study pointwise semi-slant submersions from locally product Riemannian manifolds onto Riemannian manifolds. We give example and necessary and sucient conditions for the integrability and totally geodesicness of all distributions which are mentioned in the denition of the pointwise semi-slant submersion. Moreover, we give a characterization theorem for the proper pointwise semi-slant submersions with totally umbilical bers and rst variational formula on the bers of a pointwise semi-slant submersion. In the view of that formula, nally we obtain necessary and sucient condition which is new approach to check the harmonicity of a pointwise semi-slant submersion.